Healing the next generation: an adaptive agent model for the effects of parental narcissism

Abstract

Parents play an important role in the mental development of a child. In our previous work, we addressed how a narcissistic parent influences a child (online/offline) when (s)he is happy and admires the child. Now, we address the influence of a parent who is not so much pleased, and may curse the child for being the reason for his or her unhappiness. An abusive relationship with a parent can also cause trauma and poor mental health of the child. We also address how certain coping behaviors can help the child cope with such a situation. Therefore, the aim of the study is threefold. We present an adaptive agent model of a child, while incorporating the concept of mirroring through social contagion, the avoidance behaviors from a child, and the effects of regulation strategies to cope with stressful situations.

Full text

Jabeenetal. Brain Inf. (2021) 8:4
https://doi.org/10.1186/s40708-020-00115-z
RESEARCH
Healing thenextgeneration: anadaptive
agent model fortheeects ofparental
narcissism
Fakhra Jabeen* , Charlotte Gerritsen and Jan Treur
Abstract
Parents play an important role in the mental development of a child. In our previous work, we addressed how a
narcissistic parent influences a child (online/offline) when (s)he is happy and admires the child. Now, we address the
influence of a parent who is not so much pleased, and may curse the child for being the reason for his or her unhap-
piness. An abusive relationship with a parent can also cause trauma and poor mental health of the child. We also
address how certain coping behaviors can help the child cope with such a situation. Therefore, the aim of the study
is threefold. We present an adaptive agent model of a child, while incorporating the concept of mirroring through
social contagion, the avoidance behaviors from a child, and the effects of regulation strategies to cope with stressful
situations.
Keywords: Narcissism, Parental influence, Reified architecture, Social contagion, Adaptive agent
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1 Introduction
“…phenomena are best understood when placed
within their series, studied in their germ and in their
over-ripe decay.” [1]
e behavior of a parent can contribute significantly to
the development of a child, from childhood to adulthood,
as a parent is perceived as a role-model by a child [2].
Inspired by their parents, they often try to mimic them in
everything they do. is learning process plays an impor-
tant role in the development of their personality, and
when it comes to the parental narcissism, startling effects
can be expected [2, 3]. Hence, it would be interesting to
see whether parent behavior would make a child to put
effort to mirror the parent’s behavior or, oppositely, not
to behave like the parent [4].
In the literature, it is indicated that the self-esteem of a
child is positively correlated with the feedback received
from the approval or disapproval of a parent [5]. Nar-
cissistic parents project their inflated self-views onto
their children, who internalize these experiences in an
unconscious manner, resulting in a mimicking behavior
[4]. When children are overvalued or indicated to have
superiority over others, they tend to develop narcissism
[6]. Moreover, when it comes to the self-protection of a
highly narcissistic parent, (s)he leaves his/her children
abandoned and often treat them with aggression/abuse
[7]. e victims of unhappy behaviors or narcissistic
abuse can only survive if they are able to cope with such
situations [8, 9].
Causal modeling is a field of artificial intelligence
which can address real-world processes related to differ-
ent domains such as psychology, sociology, cognitive or
neuroscience; e.g., [10, 11]. Causal models for real-world
processes are designed to address the triggering of cer-
tain events leading to a certain behavior or a process with
certain effects. For example, how a smile on a single face
can make others smile. In our earlier work, we presented
an adaptive agent model of a child, who is influenced by
a narcissistic parent. We tried to explain that when sens-
ing that the parent is happy, a child may internalize and
Open Access
Brain Informatics
*Correspondence: fakhraikram@yahoo.com
Social AI Group, Vrije Universiteit Amsterdam, Amsterdam, The
Netherlands
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Jabeenetal. Brain Inf. (2021) 8:4
may mimic this parent. We also discussed how social
media can play a role in the reflection of such behavior
[12]. However, narcissistic parenting has a dark side as
well, which needs to be addressed. By this we mean, how
an unhappy (or angry) narcissistic parent can influence
a child. It is also interesting to see, how coping mecha-
nisms can help a child to survive.
More specifically, in this paper, in addition to the agent
model of a child who is influenced by happy parenting
(offline/online), we address (a) how unpleasant parent-
ing can influence child behaviors, and (b) how coping can
help the child. us, the paper is organized in five sec-
tions. In Sect.2, we present the state-of-the-art literature
related to the behaviors of a child when influenced by a
parent and how coping behaviors and strategies can help
in stressful situations. Section 3 presents methods and
methodologies applied along with the adaptive model of
a child. Section4 discusses the simulation experiments,
while Sect.5 discusses and concludes the paper.
2 State‑of‑the‑art literature
Much research literature is available regarding the
behavior of children, and addresses the social and men-
tal development of a child under the influence of a par-
ent [3, 6, 13]. is section presents the related work in
three streams. Firstly, it discusses the psychological and
social effects of a narcissistic parent on a child. Secondly,
it presents how a parent can influence a child’s neurol-
ogy. Lastly, it discusses coping mechanisms for parental
narcissism along with AI-based approaches available till
now.
2.1 Psychological andsocial eects ofparental narcissism
Narcissism is characterized by the mythological figure
‘Narcissus’, who fell in love with his own reflection. ere
is a clear distinction between self-esteem and narcis-
sism. e former is related to the sense of self-worth of
a person, while the latter is related to the acute concern
for self-admiration [14]. Parent–child attachment plays
an important role in the development of the psychology
and nature of a child [15]. Parental warmth and affec-
tion produce compassion, and empathy in behaviors
[15], which results in an adult with a high self-esteem. In
[6] it is described how a study was conducted with four
waves with the gap of 6 months, to study how parental
overvaluation influences a child. e results indicate that
overvaluation can induce narcissism in a child [6]. e
self-inflation hypothesis states that the over-admiration
of a child makes him perceive, how others look at them.
e processes of having a sense of superiority lead to nar-
cissism [16].
Moreover, the concept of using social media or web
playgrounds is not very uncommon in children, and is
thought to be an interesting forum [17]. Such forums
allow them to interact socially, play together, form rela-
tionships and share some exciting stuff [18] with other
peers. Mimicking behavior can be reflected while using
social media, this is because of internalizing experi-
ences which they have formed from the mutual par-
ent–child interaction [2]. Internalization experiences
cause them to form an image about themselves, which
is in a way a projection of behaviors from their caregiv-
ers (e.g., parents). Another study indicates that children
mimic the grandiosity of their mothers [4], however,
this may reduce with age or maturity [19].
While discussing the darker side of narcissistic par-
enting, a child can be affected badly during childhood
[20]. It leads to low-esteem or a diminished sense of
self [21]. ey experience trauma and may go towards
anxiety and isolation [8] or even may think of suicide
[9]. Constant anxiety and stressful situations can lead a
person to mental sickness and psychological alterations
[22]. However, researchers also proposed a few strate-
gies to live a healthy life which is only possible with the
passage of time, or when a child is able to learn and to
apply them [9].
2.2 Cognitive eects ofparental narcissism
From a cognitive and neurological perspective, paren-
tal influence is noticed from the early years of a child
[23]. Parent–child interaction has been witnessed to
produce variations in brain volume and gray matter [23,
24]. Also, another study indicates that there is more
perceptual similarity of actions between parents and
their children for certain situations [25]. is results in
the involvement of similar brain regions, for example,
within the prefrontal cortex (PFC), the temporal lobes,
and the insula, when evaluating any comment or com-
pliment [26]. Overvaluation is considered by a child as
a compliment, thus it induces reward-seeking behav-
ior, as is shown by activations in the anterior cingulate
cortex (ACC) and ventral striatum [26–28]. Moreover,
when a child uses social media, sharing certain content
takes place. Also here, the target may be to get admira-
tion or acknowledgment, so that hormones like dopa-
mine are released [27].
On the downside of the parental narcissism, a child
can feel shivers due to stress and anxiety [9]. Here,
γ-aminobutyric acid (GABA) receptors get activated
when a person is experiencing anxiety [29], while
higher levels of cortisol are observed in situations of
stress [30]. Some studies also report the feeling of guilt
or depression with the lack of satisfaction, thus leading
to anxiety; e.g., [9].
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Jabeenetal. Brain Inf. (2021) 8:4
2.3 Coping withparental narcissism
Children of narcissistic parents often suffer from life-last-
ing behavioral issues, and may have a high vulnerability
[31, 32]. ey may have experienced traumatic situations,
especially when they were unable to please their parent
[8]. As a parent–child relationship is considered as a life-
long relationship, therapies or regulation strategies should
be used to endure unpleasant parent–child experiences.
A child may seek help from others, who can be therapists
or, can learn to survive by him or herself through differ-
ent problem-solving techniques. For example, a few tech-
niques from Cognitive Behavioral erapy (CBT) can
effectively reduce depression and stress [33]. is therapy
is traditionally done by therapists, however, there are indi-
viduals who can learn it and can have the best use of it at
their own [34]. Examples are having a journal or harmo-
nizing themselves rather than becoming a scapegoat [34].
Some Artificial Intelligence-based approaches are
available to detect narcissism through text [35, 36], with-
out studying causal relationships for behaviors. Tem-
poral–causal modeling is a field which is widely used to
address causal relationships for behaviors, for example,
in biological, social or cognitive domains. It can model
how one person influences another through the concept
of social contagion. Also, it discloses how over time the
environmental factors can influence the moods, brain
and psychology of a person [11, 37]. Previously, a tem-
poral–causal model was designed for a narcissist, which
reflected how the brain of a narcissist may work, and
the reaction (s)he may show over some feedback [38].
Moreover, in our previous work, we presented an agent
model of a child, who shows a high tendency to become
a narcissist like a parent [12] or may also learn to act oth-
erwise. Here, we extend our work [12] by studying the
influence of a narcissistic parent, particularly when this
parent is not happy. Also, we address how problem-solv-
ing skills or self-therapies can help the child to survive.
3 Methods andmethodologies andtheadaptive
agent model
Causal modeling is a well-known approach in the field
of Artificial Intelligence, which is widely used to repre-
sent the causal factors underlying behaviors in the real
world. ese models have variables as their basic ele-
ments, with certain causality relations between them that
together form a causal network. Each variable represents
an occurrence of an event (e.g., “he won presidential elec-
tions” or a mental state), which leads to a change in a
certain scenario (e.g., “he became a president”) [39]. Tem-
poral–causal network modeling distinguishes itself from
static causal modeling by adding a temporal perspec-
tive to it. Moreover, adaptive temporal–causal network
models address the changes in the strength of causal con-
nections or other network characteristics over time. ey
are widely used to address a variety of neural, mental,
biological, social network models in many domains [11].
is section describes the adaptive network modeling
approach using a so-called reified or self-modeling net-
work architecture, which was used to design our adaptive
model.
A reified or self-modeling network architecture is a mul-
tilevel architecture, in which a temporal–causal network
is presented at the base level, and the adaptiveness of the
model is presented in the form of self-models at higher
(reification) levels of the architecture. e temporal–
causal model at the base level contains ‘states’ as vertices
connected with a set of ‘connections’ as edges between
them. Here states Y have activation levels Y(t) that vary
over time t. To illustrate it further, consider a connec-
tion X → Y, representing state X influencing state Y. e
activation level of Y is the result of an aggregated causal
impact via all incoming connections from states Xi. is
aggregated causal impact is computed by a combination
function, applied to the single causal impacts.
defined by the connection strengths ωXi,Y of the incoming
states Xi and their state values Xi(t) at a certain time t.
erefore, for each state Y in a temporal–causal network
model, the following network characteristics are specified:
• Connectivity characteristics: connection weights
ωX,Y
is represents how strong a state X can influence state
Y. e magnitude varies between 0 and 1, however sup-
pression from a state is represented by a negative connec-
tion weight.
• Timing characteristics: speed factors ηY
is represents how fast state Y can get influenced by
the aggregated causal impact from the incoming connec-
tions. e range is normally between 0 and 1, showing
low and high, respectively. In this way, there is no need
to assume (as in other cases often is silently done) that all
states behave synchronously with the same speed.
• Aggregation characteristics: combination func‑
tions cY(..)
is is used to compute the aggregated causal impact
of all of the incoming connections. To accomplish this,
impact
X
i,
Y
(t)
=ωXi,Y
X
i
(t)
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Jabeenetal. Brain Inf. (2021) 8:4
a predefined function (e.g., identity, alogistic, scaled
sum, and so on) from a Combination Function Library
can be used, where a custom function can also be
defined and added to this library.
e network characteristics for all states (introduced
above) define a full specification for a temporal–causal
network model which can be used as input for an
available dedicated software environment. e causal
impact on state Y at time t determines the value of Y at
time t + Δt; this is computed by:
and
where aggimpactY(t) is computed as:
Adaptivity of a network model comes in when these char-
acteristics change over time. is is represented by self-
models at higher levels, for example representing first-order
adaption principles (modeled as Level II) and second-
order adaption principles (modeled as Level III). In other
words, an nth-order adaptive network model is modeled as
an n + 1 leveled network, and can also be represented math-
ematically (Appendix). For example, an adaptive connection
weight ωX,Y is modeled by adding a self-model state WX,Y
that represents the (adaptive) value of ωX,Y. Such states,
called reification states or self-model states, are the basis of
self-models within a network that represents part of the net-
work’s own network structure by some of its states. Here, we
use a second-order adaptive reified network architecture to
address the adaptive agent of a child who is interacting with
and influenced by a parent.
3.1 Level I: thebase network level
is section presents the base network model (Level I),
which depicts the mental organization of a child under
the influence of a parent. e base network is designed
according to the literature discussed in Sect. 2 and
has 39 states, in Fig.1 shown as the base plane of the
model. A categorical explanation of each of the states
is presented in Table1. A state can have three types of
incoming connections:
• Black arrows indicating a positive connection, with
possible connection weight values between [0,1].
Y(t+�t)=Y(t)+
η
Y[aggimpact
Y
(t)−Y(t)]�t
(1)
dY(t)
dt
=ηY[aggimpactY(t)−Y(t)]
,
aggimpact
Y(t)=cY

impactX1,Y(t), ..., impactXk,Y(t)

=cY

ωX1,YX1(t), ..., ωXk,YXk(t)
.
• Purple arrows indicating a negative connection
with weight values between [-1,0].
• Green arrows show the adaptive connections which
lead to adaptive behavior and will be explained fur-
ther in Sect.3.2.
According to the literature addressed in Sect. 2, a
child can sense three kinds of inputs from his or her
surroundings:
• Happiness of a narcissistic parent.
• An angry or unpleasant behavior from a parent.
• Reactions on social media.
In Fig. 1, only two states of a narcissistic parent are
shown, which act as an input to our model of a child, i.e.,
eshappy (when the parent is happy) and esunhappy (when the
parent is angry or not happy). For details of narcissistic
parent behaviors, we refer to [38].
Firstly, a narcissistic parent being happy, may stimulate
the child to mimic the parent’s behavior. is stimulus
eshappy is observed by a child, which activates the sensing
states ssh and the sensory representation states srsh. An
example can be.
“e parent looks happy when noticed in the crowd,
also a child feels good when noticed.”
In such a case, the child believes positive about himself
or herself (by cbs +); different brain parts within the PFC
and the insula are activated along with the amygdala. is
leads to the activation of feelings related to self-reward
and self-love, and make this behavior aware. As a result,
like the parent, the child exhibits narcissism: ceshappy.
is mimicking behavior is a form of social contagion.
Also, it is quite possible that a child tends not to agree
and align with the parent’s behavior, but rather acts dif-
ferently. An example can be.
“A narcissistic parent looks happy when noticed in
the crowd, however the child may prefer to remain
unnoticed.”
Understanding the narcissistic behavior and nature of a
parent comes with maturity or age and experience, mod-
eled as hipp, and as the child conceptualizes it, modeled
as evalh. erefore the child may prefer not to mimic the
parent, but rather chooses his/her own behavior which
pleases his or her mind. is also reflects that narcissism
may fade away as the child grows older and counts him or
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Jabeenetal. Brain Inf. (2021) 8:4
herself responsible for his/her own actions, modeled by
ownership state os.
Secondly, a displeased narcissistic parent may influ-
ence a child in a different way. An example can be.
“an angry narcissistic parent had some conversa-
tions with his or her child which may lead the child
towards isolation or an escape.”
is unpleasant stimulus esunhappy is sensed, via ssu
and srsu, by the child which lowers his or her esteem-
belief: cbs-. So, thinking him or herself as the source of
displeasure to the parent, the child feels rejected and
upset, causing him or her depression and stress feel-
ing fsdep and fsstress. As a result, this may lead the child
towards isolation: psiso and esiso.
Another possibility is the realization of a parent’s ‘dis-
pleasing behavior as a disease or abnormality’, modeled
by evald, which may save the child from hurting him or
herself further. is is not a one day process, rather it is
learned over time through the experience and age, due
to the parent–child relationship memories hipp2 and
the feelings of persuasiveness fsper. So, the child is con-
sciously (modeled by osavd) struggling to avoid via psavd
and esavd or trying to have some therapy to regulate him
or herself.
irdly, when using social media, a child may tend to
share some content with the influence of a narcissistic
parent under two possibilities. Either the child shares
for his or her narcissistic pleasure or if the child is not
mirroring the parent then (s)he shares his or her own
Fig. 1 Connectivity of the base level (Level I) of the network model of a child influenced by parent behavior
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Jabeenetal. Brain Inf. (2021) 8:4
expression. When encountering a post (through wss,
sss, and srss), the child can evaluate (by evals) its con-
tents ‘to be interesting’. e sharing tendency of this
content is based upon three attributes represented by
their respective feelings: novelty fsnov; emotional value
fsem attached to the content; and the urge fsurge to share
the content. ese three attributes are learnt over the
passage of time, and as a result, the child shares the
content (via psshare and esshare) over the social media.
is sharing behavior may or may not influence the
self-rewarding behavior or states of the child. It is to be
noted here that initially the child’s control state ccs con-
trols the sharing phenomena based upon beliefs influ-
enced by the parent. However, later the involvement
of the ownership state os indicates that this action is
self-attributed.
3.2 Level II: rst‑order adaption level
In this section, we will discuss the first-order adaption
level represented at Level II. It is related to the ability to
learn certain behaviors over a period of time (e.g., age/
maturity), known as plasticity or Hebbian learning [43].
In this case, the connection strengths tend to change
over time. erefore, they are represented by W-states
Wi (where i = 1 to 21) at Level II that form a (first-order)
connectivity self-model within the network. ese
W-states determine the connection strength of the con-
nections at Level I. e particular connections that are
addressed, are depicted as green arrows at Level I. As
Table 1 Categorical explanation ofstates ofthebase model (Level I)
Categories References
Stimulus states and sensing:
eshappy
esunhappy
wss
sss
srss
Narcissistic parent shows happy
Narcissistic parent shows unhappy
Using social media
Sensor state for the child for s
Representation state of the child for s
“the representation of the world external to the
body can come into the brain only via the body
itself” [40]
Social contagion related states of the child:
cbs +
cstriatum
cPFC
csfslove
cfsreward
ceshappy
Belief state of the child
Striatum: Brain part of the child
Prefrontal Cortex: Brain part of the child
Feeling of self-love (Amygdala)
Feeling of self-reward (Amygdala)
Execution state expressing happiness for the
child
“ yet familiarity.. infants copy more actions of a
familiar, compared to an unfamiliar model” [2]
“mothers show high self– child overlap in per-
ceptual similarity in the FFA regardless of their
relationship quality with their child” [25]
Non‑narcissistic behavior related states:
evalh
cpsact
cesact
hipp1
fssat
Evaluation state for analyzing behaviors
Preparation state
Execution state
Hippocampus: Brain part for memories
Feeling of satisfaction
“adolescents was associated with neural activation
in social brain regions required to put oneself in
another’s shoes” [25]
Social Media related states:
evals
os
psshare
esshare
exp
fsi
Evaluation of the input, based on belief
Ownership state
Preparation state
Execution state
Experience
Feeling states: i = novelty(nov)/emotion (em) /
urge
“Emotion then facilitates behavior that is in line
with our concerns” [41]
Unhappy reaction related states:
ssu
srsu
cbs-
fsi
evald
osavd
psi
esi
hipp2
Sensor state for sensing unhappiness
Representation state of sensed unhappiness
Low belief about himself (Low esteem)
Feeling states: i = depression(dep)/stress (str)/
persuasive (per)
Evaluation of parent as a narcissist
Ownership state of avoidance behavior
Preparation states: i = isolation (iso)/avoiding
parent (avd)
Execution states: i = isolation (iso)/avoiding
parent (avd)
Hippocampus: Brain part for memories
“Emotion then facilitates behavior that is in line
with our concerns” [41]
“children who perceived their fathers to be highly
critical.. engage in insulting name calling, and to
use guilt arousal and love withdrawal … unsta-
ble SE indicated that their fathers less frequently
talked about the good things” [42]
“the possibility of inherited narcissism and
employing narcissistic parenting strategies…
analyze themselves constantly and protect their
emotional motherhood constantly” [9]
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most states, these W-states change over time so that the
base-level connections indeed get weights that adapt over
time; this is specified according to the Hebbian learning
adaptation principle, expressed by combination function
hebbμ(..) defined at the end of Sect.3. Some of the net-
work characteristics of this first-order self-model based
on the W-states are adaptive as well, in particular, the
timing characteristics (the learning rates for the Hebbian
learning) and the aggregation characteristics (for the per-
sistency μ of the learned effects) of the Hebbian learning
modeled by this self-model; this will be discussed later in
Sect.3.3. e connectivity of the complete model with its
leveled architecture is shown in Fig.2.
To explain this behavior, consider W10 (or
W
fs
nov
,ps
share
).
Here, two states fsnov and psshare are connected through
fsnov psshare, which act as presynaptic and postsynaptic
states, respectively. e learning behavior is observed
when sending state fsnov transmits a signal to the receiv-
ing state psshare making it either more or less likely to fire
its own action potential (against a certain threshold).
ese action potentials are not fired promptly; instead,
they can last for a while before they can dissipate. Due to
this behavior, the strength of the connection fsnov psshare
can get stronger or weaker and can be learned over time
in that way. Here, the input from the connected states
to the corresponding W-state is shown by upward blue
arrows (from Level I to Level II), while the influence of a
W-state is shown by downward red arrows (from Level
II to Level I), forming a circular causation. Table2, enlist
the W-states, along with their related connections. For
more details related to the modeling such a behavior see
[11, 43].
3.3 Level III: second‑order adaption level
is level III represents the adaptation of some of the
network structure characteristics describing the first-
order self-model at the first-order adaption level, i.e.,
Level II. is makes that not only the W-states at Level
II change over time, but also the mechanism through
which the W-states change is changing. is (Hebbian
learning) mechanism may learn/adapt over time, which
represents plasticity of plasticity or metaplasticity
([45], Schmidt etal. [46]). is metaplasticity is applied
in particular to the learning rate (used at level II as a
timing characteristic of the self-model) and persistence
factor (used at level II as an aggregation characteristic
of the self-model) of the Hebbian learning mechanism.
More specifically, it is achieved by explicitly modeling
at Level III adaptive persistence factors μ and adaptive
learning rates η by second-order reification states Mj
and Hj (where j = 1 to 12) that in this way constitute a
second-order aggregation and timing self-model for the
first-order connectivity self-model at Level II. ese
states specify how the mechanism of synaptic transmis-
sion can be influenced or controlled through hormonal
release and neurotransmission [11, 45]. is second-
order adaptive behavior is modeled through upward
and downward inter-level connections, having the same
pattern as we discussed for Level I and II (Sect. 3.2).
By this we mean, that these states of second-order rei-
fication or self-model, take input from their respective
presynaptic and postsynaptic states from Level I, and
influence the involved W-states at Level II.
To illustrate it further, consider the self-model states
M10 and H10 which play an adaptive role in the dynam-
ics of W10 (
W
fs
nov
,ps
share
). ey receive a causal input
Fig. 2 Second-order reified network model of a child under the influence of a parent
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Page 8 of 20
Jabeenetal. Brain Inf. (2021) 8:4
from the respective presynaptic (fsnov) and postsynaptic
(psshare) states along with W10, which is represented by
the upward blue arrows. As a consequence (or circular
causation), states M10 and H10 determine the persistence
and speed factor of the state W10 at Level II, represented
by the red downward arrows. A lower value for H10 will
cause a lower speed for learning of the state W10, while
a lower value of M10 will be responsible to lower persis-
tence of W10 and vice versa. is will in turn control the
dynamics of the connection weights of the connection
fsnov psshare; see also [11], Ch. 4, p. 110.
e network model is simulated using the reified
network engine within the dedicated software envi-
ronment developed in MATLAB, by providing a declar-
ative specification (specifying declarative mathematical
relations and functions) for the designed agent. is
specification is in the form of role matrices, which are
given as input to the engine. Each role matrix repre-
sents the network characteristics according to the role
played with respect to a certain state. For example, for
the connectivity characteristics base matrix (mb) con-
tains for each state Y information about the incoming
connections to Y. Similarly, connection weight matri-
ces (mcwv and mcwa) indicate the connection weights
of all of the states in the model. ey can be adap-
tive by nature (specified by mcwa) or can be constant
(specified by mcwv). For the timing characteristics,
speed factor matrices msa and msv represent the adap-
tive and non-adaptive speed factors, respectively.
Finally, for the aggregation characteristics, combina-
tion function weight matrices (mcfwa and mcfwv) and
combination function parameter matrices (mcfpa and
mcfpv) specify the combination functions along with
their weights and the related parameters, respectively,
both for the adaptive and non-adaptive ones.
To illustrate the declarative specifications of the model
further, let us consider state psshare, which has 4 incoming
connections. One of them is the non-adaptive connection
evals → psshare, while the rest connections are adaptive
by nature: fsnov psshare, fsem psshare, and fsurge psshare.
So, in mb we specify the names (by their index) of all
of four states that have causal influence on state psshare.
As we have one out of four non-adaptive connections,
role matrix mcwv will only have a connection weight
for one incoming connection, i.e., for evals → psshare
(weight value = 0.5). e rest of the adaptive connections
are specified by the names (indicated by their indices)
of the respective W-states in mcwa, indicating that the
respective W-states are responsible for the change of the
connection strength over time (See Fig.2). e speed fac-
tor for psshare is specified in msv, and has the value 0.6.
e activation level for psshare is computed through the
Table 2 Explanation ofstates inlevel II andIII
States perlevel References
Level II (Plasticity/Hebbian learning for Omega states):
W1:
W2:
W3:
W4:
W5:
W6:
W7:
W8:
W9:
W10:
W11:
W12:
W13:
W14:
W15:
W16:
W17:
W18:
W19:
W20:
W21:
Wsrsh,evalh
Wbs,fslove
Wfslove,bs
Wstriatum,insula
Wfsreward,striatum
Wfslove,striatum
Wpssat,hipp
Wfssat,psact
Wpsshare,expo
Wfsnov,psshare
Wfsem,psshare
Wurge,psshare
Wcbs,dep
Wdep,cbs
W cbs,stress
Wstress,cbs
Wdep,psiso
Wstress,psiso
Wsrsu,evald
Wpsavd,hipp2
W
fs
per
,ps
avd
for srsh evalh
for cbs + cfslove
for cfslove cbs +
for cstraitum cinsula
for cfsreward striatum
for cfslove striatum
for pssat hipp
for fssat cpsact
for psshare exp
for fsnov psshare
for fsem psshare
for urge psshare
for cbs dep
for dep cbs
for cbs stress
for stress cbs
for dep psiso
for stress psiso
for srsu evald
for psavd hipp2
for fsper psavd
2–6: “Potentiation in the striatum
depends not only on strong
pre- and postsynaptic activa-
tion … reward prediction …
modify behavior” [27]
1; 7–8: “Older people,… might be
less likely to harbor narcissistic
traits. This again suggests that
narcissism should decrease with
age” [19]
9–12: “Emotion then facilitates
behavior that is in line with our
concerns” [41]
14–21:“From speech, perception,
and interpersonal interactions
with his primary caregivers, he
had to protect himself cognitive
processes, both conscious and
non-conscious” [8]
Level III (Meta‑Plasticity/Learning rate and persistence):
Mi:
Hi:Persistence
Learning rate for i = Wj: j = 1,…,12
for i = Wj: j = 1,…,12 “Metaplasticity refers to neural
changes that are induced by
activity at one point in time and
that persist and affect subse-
quently induced LTP or LTD” [44]
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Page 9 of 20
Jabeenetal. Brain Inf. (2021) 8:4
alogistic combination function which is specified through
mcfw. Finally, to set the parameters for the alogistic com-
bination function mcfpv is used, containing the param-
eter values for the alogistic function defined as:
where:
V1,…Vk represent the single impacts from the four
incoming states, i.e., from evals, fsnov, fsurge, fsem.from
evals, fsnov, fsurge, fsem.σ = the steepness (value = 10
for psshare), and τ = the threshold for the activation
(value = 0.2 for psshare).
In total, the designed network model has 84 states:
39 states at Level I, while Level II and Level III have
21W-states and 24 M- and H-states, respectively. To
compute the activations over time, we used three type
of combination functions for our network model i.e.:
a) 10 states (ssh, srsh, ceshappy, fssat, sss, srss, ssu, srsu, fsper,
esavd) use the Euclidian function, which is specified
by:
eucln,λ (V1,…,Vk) = n

(V
n
1
+··· + V
n
k
)/

,
where
n = order of the Euclidian function, and
λ = scaling factor for normalization.
b) All W-states (Wi; i = 1–21) use Hebbian learning
principle defined by:
where
µ = persistence factor for the learning,
V1 and V2 are the activation levels of the connected
states, and
W = their connection weight
ωV1,V2
.
c) Lastly, the remaining 53 states (including for the
24 states of M and H at Level III) use the alogistic
function where steepness and threshold ≤ 1, also
addressed earlier.
To get further insights into the declarative role matrix
specification format, see [11]. Also, for the full specifica-
tion of the adaptive network agent model of the child see
[12].
alogisticσ,τ
(V1,...,Vk)=[(1/(1+e
−σ(V
1
+...+V
k
−τ)
)) −1/(1+e
στ
)](1+e
−στ
)
,
hebbµ(V1,V2,W)=V1V2(1−W)+µW,
4 Simulation experiments
Setting up the simulation experiments enables research-
ers to study and analyze the dynamics of any real-world
scenario they want to consider. In this section, in par-
ticular, we will study the dynamics of our agent model
of a child under the parental influence. First, we will
address how a child may behave when he senses the hap-
piness or unhappiness of a narcissistic parent. Second, it
will be addressed how a child behaves when he is using
social media under the parental influence. ird and last,
we address how a child can learn to cope with a narcis-
sistic parent. One thing to be noted is that we will not
discuss the behavioral changes of a parent as they are
already addressed in detail in [38]. erefore, this section
is divided into three subsections with respect to different
behaviors of a child:
a) A child has a strong tendency to exhibit similar
behaviors like the parent,
b) A child shows resistance to imitate the parent behav-
ior, and
c) A child trying to cope with an unhappy narcissistic
parent.
4.1 Exhibition ofnarcissistic behaviors
Here, we present the behaviors of a child who is influ-
enced by a parent. We will discuss how a happy parent
nurtures narcissism in the child from childhood to adult-
hood years. We will discuss two scenarios: (a) parental
influence without the digital world and (b) with the digi-
tal world.
4.1.1 Parental Inuence ‘o’ thedigital world
Most of us are aware of the idiomatic expression ‘like
mother, like daughter’. Consider a child whose parent is
a TV actor or a renowned one, always seeking appraisal
and love from the society, in such a situation the child
would also like to mimic that parent.
Figure 3 shows the simulation of such an interac-
tion between the parent and child over time. e child
senses when the parent is the center of attention and
looks happy (state eshappy tends to get a high value of
0.95 at time point t = 25), which is sensed through the
child’s sensor state ssh deep orange) and representation
state srsh (mustard). e child’s main source for learn-
ing human behaviors is in early years of age, and the
main source to learn is from the parent or caretaker (so
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Jabeenetal. Brain Inf. (2021) 8:4
considering wss = 0). e fostering behavior of the par-
ent makes the child feel positive about him or herself,
which influences the child in two ways: (a) it raises the
esteem/belief state cbs + (purple) of the child. Secondly,
the child realizes/conceptualizes through the prefrontal
cortex state cPFC (green) and makes feel as ‘valuable’ at
t = 11. So, under the parental influence, the child starts
to mimic the parent around time point t = 15–50, feels
rewarded (cstriatum: brown bold), and is happy about it
(ceshappy: mustard bold). However, until now the child is
just reflecting his parents’ social behaviors, so the own
feelings related to self-rewarding behavior are not acti-
vated yet. is mimicking behavior stays till t ≈ 280, so
the values for the both of the states stay till 0.5.
After time point t = 280, the feelings of self-reward
(fsreward: greyish blue) and self-love(fslove: maroon) start
to increase, due to the activations in insula (cinsula: light
blue). is behavior is expected, as the child is also learn-
ing (via W4) that mimicking the parent can be rewarding.
At this point, the child starts to reflect the learned nar-
cissism by his or her behaviors (social contagion). ere-
fore, activations in the self-rewarding states (fsreward, fslove,
cinsula, along with cstriatum) cause the states cstriatum
and ceshappy to get elevated (value > 0.95) at time point (t
≈ 300). It is to be noted that the belief state also reflects
the learning behavior over time, and therefore it also goes
to value = 1 at time point t = 290–300, showing that the
child has become a narcissistic soul.
Here, the dotted lines show the dynamics of the con-
nection weights through Wi states, where i = 2, 3, 4,
5, and 6. ese dynamic states reflect the hebbian
learning behavior, for example it can be seen that W4
(Wstriatum,insula) starts to grow at t > 50, as it is responsi-
ble for the child’s awareness [47]. is influences W5 and
W6 (i.e.,
Wfsreward,striatum
and
Wfslove,striatum
) to learn over
of time. Similarly, state W2 (
Wbs,fslove
) and W3 (
Wfslove,bs
)
reflect the same behaviors around time t ≈ 280, which
determine the adaptive connections (cbs cfslove and
cfslove cbs) at Level I.
To illustrate the control over the dynamics of W-states
from Level III, it is nice to observe the role of the M- and
H-states, which are shown by a dotted line and a line
marked with stars, respectively. For example, by looking
into W4, it can be observed that M4 and H4 reach high
values (> 0.9) causing W4 to elevate at a faster speed than
the rest of the W-states. As part of the circular causation,
this influences the activation of the related postsynap-
tic state (i.e., insula), which in turn influences the other
states (cfslove, cfsreward). ese activations, make it possi-
ble for ‘neurons that fire together wire together’. us the
activations in the respective M- and H-states enable to
gain the connection strengths in: W2, W3, W5 and W6. As
a combined effect, a sudden increase in W3, W5 and W6
can be observed at Level II between t = 250–300 (dotted
lines). As a result, the respective connections get strong
thus showing at Level I the social contagion behavior of a
child (narcissistic influence).
4.1.2 Parental Inuence ‘on’ thedigital world
Here, we discuss the behavior of a child, who start using
a social media apps (like Disney’s Club Penguin /Twit-
ter/WhatsApp and so on), and is influenced by a happy
Fig. 3 Child is mimicking his/her parent’s behavior as (s)he senses happiness (input: eshappy), along with learning
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Jabeenetal. Brain Inf. (2021) 8:4
narcissistic parent (eshappy = 1). To see how sharing over
social media influences behavior of a child over time,
we present the simulation in episodes. e two episodes
include when a child (a) is not using social media, and
(b) when (s)he is using social media. Each episode is dif-
ferentiated by different colors such that, the episodes
with white background show the behavior of a child
while not using social media, for example, first episode
is from t = 0–60. In contrast episodes with the colored
background show the behavior when the child is using
the social media, for example, from t = 60–120. It is to be
noted that, length and duration of the episodes may vary
and can be overlapping as well, however, for the sake of
simplicity we kept them non-overlapping and with equal
intervals (see Fig.4).
e simulation starts with the episode when the child is
‘not using the social media’. e child already shows some
influence of the parent before time point t = 60, through
activations of self-rewarding states (bold curves—cstria-
tum: purple; ceshappy: green; cinsula: cyan). e new epi-
sode starts when the child starts using social media (i.e.,
wss = 1) at t = 60. An example can be ‘looking at a post’,
this will activate the child’s sensor state sss (orange) and
representation states srss (yellow) around t = 61–65.
After looking at the contents, the child evaluates it as an
‘attraction seeking content’ of the post, this activates his
or her evaluation state evals (green), along with the con-
trol state ccs (purple), which is responsible to conceptu-
alize the content. After evaluation, the child shares the
content if it fulfills his or her criteria, which can be nov-
elty, associated emotion and urge. By this we mean, if the
child has a feeling that the content is novel (fsnov: brown
dotted), and have some emotional association (fsem: red),
the child’s urge (fsurge: dark blue dotted) to share the con-
tent gets higher. is criterion is learned by prior experi-
ences and memories (exp: light blue dotted). An example
of experience can be.
“which kind of posts gained maximum attention.”
An increase in the reward-related states is clearly
observed here as well. Rather it would not be wrong to
say that during the second episode: t = 120–180, the
self-rewarding states seem lesser suppressed than the
previous episode (t = 60–120). Clearly, this reflects the
presence of attention-seeking behavior of the child or
in other words, he is sharing the content for his narcis-
sistic pleasure. Similar behavior is observed, till the self-
rewarding states reach to their maximum value (value
≈1). It is interesting to observe that, unlike all other
states, urge fsurge to share the content does not drop to
0, while the child is not using social media. is make
sense as the child enjoyed sharing the content, so (s)he
will have an ongoing urge to use social media, and to get
attention from his or her peers.
Interestingly, the effect of hebbian learning can natu-
rally be seen in the alternative episodes, through differ-
ent intensities or activation levels of the involved states.
However, Fig.5 provides more insights on the dynamic
Fig. 4 Episodes showing the behavior of the child while a not using social media, and b while using social media, with the tendency of the
exhibition of parental narcissism
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Jabeenetal. Brain Inf. (2021) 8:4
connection weights, which are changing over time. Here,
the W-states related to self-rewarding behavior (Wi:
i = 2–6) continue to learn over time. It can be observed
that there is a sudden increase in W4 (i.e., Wstriatum,insula)
from t > 100 indicating that the child is getting aware of
the self-rewarding behavior. is learning plays a vital
role in activation and learning of the corresponding feel-
ings (fsreward,fslove), and their connections through W5
(
Wfsreward,striatum
) and W6 (
Wfslove,striatum
) and so on.
While looking at the W-states related to the episode of
‘sharing content’ (i.e., Wi: i = 9–12), we can see a gradual
increase of almost all of the states from t = 0–450 till they
reach to their maximum. However, this is not true for the
W12 (
Wurge,psshare
) as it drops to 0 in each episode of ‘not
using the social media’, for example during t = 120–180;
240–300; and so on. e reason is that the urge of sharing
content is almost new at the start of each episode (/expo-
sure to social media) until he is a regular user of social
media. By adjusting the H- (dotted lines) and M-states
(small dots) for the W-states, learning can be controlled
so that it accelerates or decelerates. e variations in rei-
fication states M for persistence and H for learning speed
Fig. 5 W-states during the alternative episodes addressed in Fig. 4
Fig. 6 Dynamics observed when the child learns to be non-narcissistic given (s)he senses happiness (input: ehhappy)
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Jabeenetal. Brain Inf. (2021) 8:4
factor have their controlling effect on the dynamics of
the respective W-states. It can be seen that, Hi and Mi
(i = 9–12), show elevation with time. For example, with a
gradual increase in W11 (
W
fs
em
,ps
share
:black) after t > 60, a
periodic pattern is observed M11, indicating that in every
episode of ‘a child using the social media’, the child is
learning to establish an emotion related to some content
(persisting the past experiences). However, W11 is able to
reach its maximum value due to hebbian learning once
H11 reaches its maximum value. e faster (learning)
speed for W11 is also reflected in fsem psshare.
4.2 Exhibition ofnon‑narcissistic behaviors
Here, we present how a child though nurtured by a
narcissistic parent, blooms to his or her full potential.
erefore, in this section, we address two scenarios: a)
how a child gains maturity with time, and b) how the
digital world influences the child.
4.2.1 Maturity andtheparental inuence ‘o’ thedigital
world
According to Samuel Ullman
“maturity is the ability to think, speak, and act
your feelings.”
In this section, we present the simulation where a child
notices that his parent is a narcissist but resists to act like
one. An example can be
“in a social gathering, unlike his parent, he prefers to
remain unnoticed.”
is scenario is addressed in Fig. 6, when a child
starts getting the stimulus from a happy parent (eshappy:
blue), around time t < 25. e child senses (ssh: brown;
srsh:mustard), and starts to learn about the parent’s
behavior by the evaluation state evalh (purple). is
learning enables the child to act (cpsact: green; esact: light
blue) in such a way, which can please his or her own soul
(fssat: deep blue), rather than mirroring the parent, i.e., in
a non-narcissistic way. An example can be.
“sitting on a couch, where no one notices him/her.”
e feeling of self-satisfaction comes with the past
experiences and memories (hipp1: maroon), which he
had over time.
Here, the learning of the connection weights (W-states)
is shown by the dotted bold curves. It can be seen that
W1 (
Wsrsh,evalh
:magenta) starts to learn around t ≈ 25,
causing W7 (
Wpssat,hipp
:mustard), and W8 (
Wfssat,psact
:
purple) to learn as well by the time point t = 100. is
learning behavior also can be observed through the acti-
vation levels of the action related states, i.e., psact (green)
and esact (blue). Here, it would be interesting to observe
the ‘unlearning behavior’ of W1 (
Wsrsh,evalh
) and W8
(
Wfssat,psact
). By this we mean the dip in the two curves,
which shows that the child unlearns the behaviors related
to self-satisfaction and evaluation from the past experi-
ences and memories. Please note, W7 (
Wpssat,hipp
) does
not show the same dip, which explains the learning
of experiences in the child’s life over time. is is also
observed through M- and H-states (small dotted curve)
which play their role in controlling the elevation of the
W-states. One thing to be noted here is that Mi (i = 7, 8)
are initially set to 1. However, it would be interesting to
note that, as the child is not satisfied initially, the values
go down, and then the child learns the behavior which
Fig. 7 W-states during the alternative episodes addressed in Fig. 8
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Jabeenetal. Brain Inf. (2021) 8:4
can satisfy him or her. e possible reason can be that
the child was satisfied before (s)he started to evaluate the
parent’s behavior. As the evaluation process starts and
the child is going towards the action that can satisfy his/
or her own soul, these states are increasing effecting the
respective W-states (hebbian learning).
4.2.2 Non‑narcissistic behaviors ‘on’ thedigital world
In this section, we will see how the usage of social media
does not elevate narcissism in a child under influence of
a parent. To understand the learning behaviors, we again
present episodes where: (a) a child is not on social media,
and (b) a child is using social media.
Most of the curves tend to show the same behavior like
in Fig. 4, except for the self-rewarding behavior. Here,
the activation levels of the related states do not vary over
time (striatum; cinsula; ceshappy; value = 0.42). Moreo-
ver, the learning behaviors of the W-states can be seen
in Figs.7 and 8 as well, where no dynamics are observed
for W2 (
Wbs,fslove
) and W3 (
Wfslove,bs
) showing there is
no activation for self-love (Fig.8). is indicates that the
child likes to share the content and feels happy like every
child, but has less tendency of turning into an attention
Fig. 8 Episodes showing the behavior of the child while a) not using the social media, and b) while using the social media, without the tendency of
narcissism
Fig. 9 Behavior of an isolated child after the narcissistic abuse (input: esunhappy)
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seeker or a narcissist as there is no gain in self-love. For
Level III activation, they are similar to Fig. 5, however,
as there is no learning for self-rewarding behavior, the
related M- and H-states remain constant along with the
W-states.
4.3 Coping withanarcissistic parent
e simulations presented in Sect. 4.1 and 4.2 showed
the behavior of a child while sensing the happiness of a
narcissistic parent. What if the child is dealing with an
unhappy parent or is facing an unpleasant situation? In
this section, we will discuss what impression an unhappy
parent can leave on the child’s brain. Also, we will address
how the child can learn to cope with such a situation.
erefore, this section is divided into two subsections: (a)
how an unhappy narcissistic parent influences the child,
and (b) what can the child do to survive.
4.3.1 Unhappy face ofanarcissistic parent
Literature shows that living with narcissistic abuse can
be hazardous for mental and physical health [32, 34].
Consider a scenario which explains such a parent–child
relationship:
“I was taken to a hospital when I was complain-
ing about stomach and articular pain. I felt being
under everyone’s feet and guilty of existing. I
thought everyone would be better if I did not exist.
I thought about suicide first time when I was nine.
I just did not know how to do it.” [9]
Or, another example scenario can be:
“You dare not to express your feelings and you do
not have sufficient connection with your emotions
or yourself when a child or even as an adult. You
learn how to hide your creativity and strength
because they are being nullified, even envied at
home.” [9]
In order to explain such a scenario through simula-
tion experiments, consider Fig.9. Here, an unpleasant
behavior (esunhappy: blue) of a narcissistic parent acts
as a stimulus at t < 10. The child senses the stimulus
through sensor state ssu (brown) and sensory repre-
sentation srsu (mustard) states at time point t < 25. As
addressed in the example, such behaviors make the
child think for being responsible for every bad thing
which can happen in the parent’s life. This may result
in low esteem shown by cbs- (purple). Narcissistic
abuse produces stress and depression (dep: deep blue),
and as a result the child gets isolated (psiso: magenta
bold; esiso: green) from the parent as well as from the
society, making the stress and depression elevated.
Here, hebbian learning of W-states: Wi (where
i = 13—18) is also shown by dotted lines. These states
do not change till t ≈ 80. However, when the child
starts to get isolated, the Wi (i = 13—18) goes high, so
are the involved states, i.e., depression (dep) and stress.
4.3.2 Coping withtheunhappy face
Much research is done on how to cope with narcissists
and to lead a healthy life [32, 34]. In this section, we pre-
sent a scenario in which a child is learning to cope with
the unhappy behavior of a narcissistic parent. A parent
Fig. 10 Coping with the narcissistic parent while (s)he is unhappy (input: esunhappy)
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Jabeenetal. Brain Inf. (2021) 8:4
can be displeased by any situation around, which is caus-
ing mental distress to the child as well. However, when a
child recognizes the narcissistic face of the parent, (s)he
can cope with this pain. An example of self-supporting/
coping behavior can be:
“After finding the illness called narcissism, I have
been able to be stronger in front of my mother.” [9]
Or, another example scenario can be:
“e actual change toward better life started to hap-
pen when I moved away from my home place, to
over 900km away to study.” [9]
Figure10 shows a simulation of the behavior of such a
child. Whenever a parent shows displeasing behavior to
the child (esunhappy: blue), the child senses it (ssu: brown;
srsu: mustard). Gradually, the child evaluates and learns
to recognize it as an intense displeasure displayed by the
parent who is a narcissist, through the child’s evaluation
state evald (purple dotted) around time point t = 25–70.
e child realizes the parent’s nature, so starts to avoid
the parent (psavd: bold blue; and esavd: bold green). is
is a conscious step which the child takes to survive, rep-
resented by the ownership state osavd (maroon). Another
example of avoidance behavior (avoidance strategy) can
be something like:
“In order to survive, you have to shrink yourself
when near a narcissist.” [9]
Or the child can choose to modify the situation (situa-
tion modification) to solve this problem like:
“I have chosen such work fields and places that have
needed me working in shifts all the time. So that I
could be away from home. If I tell her I am at home
during the weekdays, she can call me 5 am asking
for help. I went to work on sea so that I could not
be reached at all. I worked at the ship for two years
non-stop.” [9]
To survive, the child acts in a persuasive manner, so
has to stay and feel firm (fsper: blue) in his or her actions.
Also escaping from the parent makes him learn differ-
ent workouts with different experiences and memories
(hipp2: green), related to survival with the hot-headed
parent. is is represented by the learning of connection
weights, Wi (i = 19–21) from time point t = 45 for W19
(
Wsrs,evald
: orange dotted), which gradually increases with
time.
4.4 Eects ofcoping behaviors
To break the cycle of continuous stress and anxiety,
a child needs to learn for self-support and go for some
problem-solving techniques by him or herself, or by the
help of a trust-worthy person. Some examples of such
techniques can be keeping a journal to identify behavio-
ral changes for him or herself and for the parent. Another
can be doing the deep breathing exercises or mindful-
ness, for example:
“Nature and nearby woods offered me a safe place to
be. I used to play in the woods often alone. I thrived
smelling the woods only because nothing in there
intimidated or blamed me.” [9]
e effects of such problem-solving techniques can be
observed by the simulation addressed in Fig.11. Initially
Fig. 11 Coping behaviors reduce stress and depression/anxiety caused by narcissistic abuse
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Jabeenetal. Brain Inf. (2021) 8:4
as addressed in Sect.4.3.1 (white background), the child
is feeling depression (dep: bold green) and stress (stress:
bold blue). However, around time point t = 400 (colored
background), the child learns to conceptualize the behav-
ior of the parent (eval: purple dotted). As a result, the
subsequent states psavd (blue), osavd (maroon), hipp2
(green), and esavd (bold green) are activated. At this point
the opted strategy can be the choice of problem-solv-
ing technique (like breathing, mindfulness, and so on)
through preparation and execution states psavd (maroon)
and esavd (blue) after t = 400. As an effect of activation of
esavd, a gradual decrease can be observed in the levels of
stress (bold blue) and depression/anxiety (dep:green).
e firmness of the coping behavior can be reflected in
Fig.12, which shows the scenario addressed in Sect.4.3.2
No further learning can be observed, due to past experi-
ences and memories, so the states related to the child’s
behavior gains equilibrium (therefore Eq. 1 becomes:
Y(t + Δt) = Y(t)) without showing any further dynam-
ics. is indicates that the child has learned the coping
behaviors for his or her endurance.
5 Discussion andconclusion
In this study, we presented an adaptive agent model of
a child, who is influenced by a parent modeled as a sec-
ond-order adaptive network model. It addresses adap-
tive cognitive and social processes, which are involved in
preparing a child to act in a narcissistic or non-narcissis-
tic way. We presented three types of behaviors through
simulation experiments. Firstly, we presented how a child
can learn to act in a narcissistic way. is is discussed
under the parental influence while (a) being offline and;
while (b) using the social media. It was observed, that
in both of the scenarios nurturing behavior of a parent
was reflected and the child tried to imitate the parent’s
behavior both online and offline. Secondly, we showed
how kids can behave in a non-narcissistic way under
the parental influence. To address this, (a) we presented
the child’s learning behavior in which (s)he chooses not
to be like the parent and (b) change of behavior while
using or not using social media. In these scenarios, it was
observed, that the child did not go for narcissistic pleas-
ure, but tried to opt for the choices in which (s)he was
not imitating the parent. Lastly, we presented how an
unpleasant behavior of a narcissistic parent can influence
the child, and how different regulation strategies can help
the child to recover from such a situation.
Our work has some limitations, we did not study many
other factors that can influence a child along with the
parental influence. For example, how the social relation-
ship of a child with other family members or friends can
influence him. Another example can be how the sensi-
tivity/vulnerability of a child can influence him or her.
Also, it would be interesting to see how child narcissism
can influence a parent and how this loop will go on, or
how personality development programs can influence
the child. Moreover, this model needs to be validated
through the empirical data according to the designed
model. Although, some psychological studies are availa-
ble with data related to child narcissism; however they do
Fig. 12 Child trying to cope with a firm behavior, showing no further dynamics
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Jabeenetal. Brain Inf. (2021) 8:4
not mention any details with reference to the narcissism
of the parents [6] or they are not changing over time [32].
erefore, as the future work of our study, we aim to
look into other psychological and social aspects of the
behavior of a child, with a narcissistic parent. Moreover,
we would also like to incorporate other factors like sensi-
tivity or vulnerability of a child. Moreover, we would like
to collect and study empirical data to validate our model.
is validation process would reveal further behaviors of
a child. In the end, by studying these behaviors, we aim
to design and investigate the support strategies further,
which can provide support to such a child, to become a
better human.
Abbreviations
ACC : Anterior Cingulate Cortex: Brain Part; GABA: γ-aminobutyric acid; CBT:
Cognitive Behavioral Therapy; ws: World state; ss: Sensory state; srs: Sensory
representation state; evalh: Evaluation state of happiness; evald: Evaluation
state of disorder; cbs: Child belief state; PFC: Prefrontal Cortex: Brain Part;
os: Ownership state; ps: Preparation state; es: Execution state; act: Action; h:
Happiness; u: Un-happiness; fs: Feeling state; hipp: Hippocampus: Brain Part;
sat: Satisfaction; exp: Experience; nov: Novelty of content; em: Emotional asso-
ciation with the content; urge: Urge associated with the content; cs: Control
state; dep: Depression related state; stress: Stress related state; avd: Avoiding
a situation.
List of symbols
μ: Persistence; ηY: Speed factor of state Y; ωX,Y: Connection weight of a connection
from X to Y; cY: Combination function for state Y; Pi,j: Combination function param-
eter reification; W1;
Wsrsh,evalh
: Reification state for the weight of the connection
srsh→evalh; W2;
Wfslove,bs
: Reification state for the weight of the connection
fslove→cbs+; W3;
Wbs,fslove
: Reification state for the weight of the connection
cbs+→fslove; W4;Wstriatum,insula: Reification state for the weight of the connection
striatum→insula; W5;
Wfsreward,striatum
: Reification state for the weight of the
connection fsreward→striatum; W6;
Wfslove,striatum
: Reification state for the
weight of the connection fslove→ striatum; W7;
Wfssat,hipp
: Reification state for
the weight of the connection fssat → hipp; W8;
W
fs
sat
,ps
act
: Reification state for
the weight of the connection fssat→ pssat; W9;
Wpsshare,exp
: Reification state for
the weight of the connection psshare→exp; W10;
W
fs
nov
,ps
share
: Reification state
for the weight of the connection fsnov→ psshare; W11;
W
fs
em
,ps
share
: Reification
state for the weight of the connection fsem→ psshare; W12;
Wurge,psshare
: Reifica-
tion state for the weight of the connection urge→ psshare; W13;Wcbs,dep: Reification
state for the weight of the connection cbs→ dep; W14;Wdep,cbs: Reification state
for the weight of the connection dep→ cbs+; W15;Wcbs,stress: Reification state for
the weight of the connection cbs+→stress; W16;Wstress,cbs: Reification state for the
weight of the connection stress→ cbs+; W17;
W
dep,ps
iso
: Reification state for the
weight of the connection de→ psiso; W18;
Wstress,psiso
: Reification state for the
weight of the connection stress→ psiso; W19;
Wsrsu,evald
: Reification state for the
weight of the connection srsu→ evald; W20;
W
ps
avd
,hipp
2
: Reification state for
the weight of the connection psavd→ hipp2; W21;
W
fs
per
,ps
avd
: Reification state
for the weight of the connection fsper→ psavd; M: Reification state for the persis-
tence; H: Reification state for the speed factor; love: Self-love; reward: Self-reward.
Acknowledgements
The first author is grateful to Vrije Universiteit Amsterdam and University of the
Punjab for providing me opportunities for my research career.
This is an extended version of our paper ‘Are we Producing Narci-nials? An
Adaptive Agent Model for Parental Influence’ [12] that appeared in the Brain
Informatics conference in 2020, and is invited for Brain Informatics journal—
BRAI. The new content (roughly 140% extra) of this article is an extension of
the model with a wider perspective. Initially, we discussed only the online and
offline behaviors of a child who was admired by a narcissistic parent. Here it
is extended to incorporate how an unpleasant parent can influence a child,
along with how coping mechanisms can help to heal him or her.
Authors’ contributions
FJ being a Ph.D. student presented the idea and completed the modeling and
experiments, while CG and JT being supervisors, supported the design of the
study and helped towards completion of the project and producing the final
manuscript of the paper.
Funding
Overseas scholarship from University of the Punjab, Lahore Pakistan.
Availability of data and materials
The data and materials used for analysis and development of results is avail-
able here.
Competing interests
The authors declare that they have no competing interests.
Appendix
Numerical relevance ofthemodel
e mathematical representation of a reified or self-mod-
eling network architecture in terms of its network char-
acteristics can be explained as follows [11]:
1. At every time point t, the activation level of state Y at
time t is represented by Y(t), with the values between
[0,1].
2. e single impact of state X on state Y at time t is
represented by impactX,Y(t) = ωX,Y X(t); where ωX,Y is
the weight of connection X → Y. All single impacts
for a given state Y are aggregated by a combination
function cY(..); see below.
3. Specific states are used to model specific types of net-
work adaptation, where network characteristics such
as connection weights or combination functions are
dynamic. For example, WX,Y represents an adaptive
connection weight ωX,Y (t) for the connection X → Y,
while HY represents an adaptive speed factor ηY(t)
of state Y. Similarly, Ci,Y and Pi,j,Y represent adaptive
combination functions cY(.., t) over time and their
parameters, respectively. Combination functions are
built as a weighted average from a number of basic
combination functions bcfi(..) from a library, which
take parameters Pi, j,Y and values Vi as arguments. For
adaptive network models in which network charac-
teristics are dynamic as well, the universal combina-
tion function c*Y(..) used for any state Y is defined as:
where at time t:
c∗
Y(S,C1, ..., Cm,P1,1,P2,1 , ..., P1,m,P2,m,V1, ..., Vk,
W
1, ..., Wk,W)=W+S[C1bcf1(P1,1,P2,1 ,W1V1,...,WkVk
)
+... +Cmbcfm(P1,m,P2,m,W1V1, ..., WkVk)]/
(
C
1+
...
+
C
m)−
W
]
,
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Page 19 of 20
Jabeenetal. Brain Inf. (2021) 8:4
• variable S is used for the speed factor reification
HY(t).
• variable Ci for the combination function weight reifi-
cation Ci,Y (t).
• variable Pi,j for the combination function parameter
reification Pi,j,Y(t).
• variable Vi for the state value Xi(t) of base state Xi.
• variable Wi for the connection weight reification
WXi ,Y(t).
• variable W for the state value Y(t) of base state Y.
4. Based on the above universal combination func-
tion, the effect on any state Y after time Δt is com-
puted by the following universal difference equation
as:
which also can be written as a universal differential
equation:
Received: 15 October 2020 Accepted: 25 October 2020
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