Fahimeh Nazarimehr

• PHD
• PhD at Amirkabir University of Technology

Analysis of a dynamic system helps scientists understand its properties and utilize it properly in different applications. This study analyzes the effects of various external excitements on a recently proposed mathematical neuron model derived from the original Fitzhugh–Nagumo model. Different bifurcation analyses on this system are conducted to de...

Swarmalators are entities that combine the swarming behavior of particles with the oscillatory dynamics of coupled phase oscillators and represent a novel and rich area of study within the field of complex systems. Unlike traditional models that treat spatial movement and phase synchronization separately, swarmalators exhibit a unique coupling betw...

Epilepsy is a multifaceted neurological condition marked by repetitive seizures that arise from irregular electrical activity in the brain. To understand this condition, a thorough examination of brain signals captured in different states is needed. In order to examine the dynamic behavior of brain signals in three different conditions: healthy, se...

Deception detection is a critical aspect across various domains. Integrating advanced signal processing techniques, particularly in neuroscientific studies, has opened new avenues for exploring deception at a deeper level. This study uses electroencephalogram (EEG) signals from a balanced cohort of 22 participants, consisting of both males and fema...

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which c...

Various regimes of a ring of non-identical attention deficit disorder (ADD) models are studied in this paper. The ADD model used in this paper can show multistability. The dynamics of the coupled maps are investigated by changing the coupling strength and parameter mismatch. In this study, a similarity function is used for the lag synchronization a...

Swarmalators, which combine the swarming phenomenon with synchronization, have drawn a lot of attention from researchers in recent years. Nevertheless, the majority of earlier research contends with identical swarmalators, thus neglecting dynamics that might emerge with parameter heterogeneity. In this paper, we therefore study the internal dynamic...

This research presents a method to encrypt and compress images using two-dimensional sparse decomposition, chaotic systems, and convolutional layers. The original image is first encrypted via the convolutional layers in the proposed approach, inspired by deep neural networks. This step is called CLE, which stands for convolution layer-based encrypt...

To examine the hemostatic behaviors of neural activity and extracellular matrix (ECM) molecules, this paper provides a mathematical model for ECM combined with a FitzHugh–Nagumo neuronal model. The dynamic behaviors of the proposed model are investigated utilizing dynamical tools such as Lyapunov exponents and bifurcation diagrams. The basin attrac...

Investigating the time–frequency-based phase synchronization between nonstationary time series of the cryptocurrencies’ prices can be a suitable tool to reveal their complicated interactions at different frequencies. In this work, the phase synchronization between 25 cryptocurrencies with the highest capitalization from December 1, 2021 to June 1,...

Several mathematical models, such as Hodgkin–Huxley, FitzHugh–Nagumo, Morris–Lecar, Hindmarsh–Rose, and Leech, have been proposed to explain neural behaviors. Changing the parameters of neural models reveals the various neural dynamics. To make these models as realistic as possible, they should be studied in the networks, where there are interactio...

A hyperchaotic system with fractional terms and fractional-order derivatives is investigated in this paper. Simulations show that different attractors such as equilibriumpoint, limit cycle, and hyperchaotic attractor can be generated by the system. Circuit of fractional-order integrator is designed and used to implement the circuit of the studied s...

Transitions from incoherent to coherent dynamical states can be observed in various real-world networks, ranging from neurons to power-grids. These transitions can be explosive or continuous, with far-reaching implications for the functioning of the affected system. It is therefore of the utmost importance to determine the conditions under which su...

This paper introduces a new 3D conservative chaotic system. The oscillator preserves the energy over time, according to the Kaplan–Yorke dimension computation. It has a line of unstable equilibrium points that are investigated with the help of eigenvalues and also numerical analysis. The bifurcation diagrams and the corresponding Lyapunov exponents...

We study the synchronization properties of a generic networked dynamical system, and show that, under a suitable approximation, the transition to synchronization can be predicted with the only help of eigenvalues and eigenvectors of the graph Laplacian matrix. The transition comes out to be made of a well defined sequence of events, each of which c...

In this paper, we propose a time-varying coupling function that results in enhanced synchronization in complex networks of oscillators. The stability of synchronization can be analyzed by applying the master stability approach, which considers the largest Lyapunov exponent of the linearized variational equations as a function of the network eigenva...

In this paper, the behavior of a 1D chaotic map is proposed which includes two sine terms and shows unique dynamics. By varying the bifurcation parameter, the map has a shift, and the system's dynamics are generated around the cross points of the map and the identity line. The irrational frequency of the sine term makes the system have stable fixed...

This topical issue collects contributions of recent achievements and scientific progress related to the collective behavior of nonlinear dynamical oscillators. The individual papers focus on different questions of present-day interest in this topic.

Synchronization is one of the interesting collective behaviors of oscillators. It refers to a phenomenon in which some dynamically connected systems behave the same. In dynamic systems, as the bifurcation points of the system approach, the system slows down and returns to its steady-state later with a slight disturbance. The system's slowness befor...

The time series of cryptocurrency prices provide a unique window into their value and fluctuations. In this study, an ordinal partition network is constructed using the price signals, and its features are extracted to investigate the variations. Our research shows that the proposed method indeed works well for analyzing price fluctuations. We apply...

The study of synaptic connections offers valuable insights into neuron interactions. It can demonstrate the neurons’ collective behaviors, like synchronization. In this paper, the dynamics of two coupled neurons in three different synaptic connections are studied: electrical, chemical, and electrochemical. The Chay neuron model is explored, and its...

A megastable oscillator with various types of attractors is proposed. The oscillator shows interesting dynamics like cloud, kite, and arrow-like attractors. As we know, such a megastable oscillator with the dynamic shapes was not previously reported. There is an infinite number of arrow-like attractors in this oscillator. Investigating equilibrium...

In this study, an epidemic model for spreading COVID-19 is presented. This model considers the birth and death rates in the dynamics of spreading COVID-19. The birth and death rates are assumed to be the same, so the population remains constant. The dynamics of the model are explained in two phases. The first is the epidemic phase, which spreads du...

Data security represents an essential task in the present day, in which chaotic models have an excellent role in designing modern cryptosystems. Here, a novel oscillator with chaotic dynamics is presented and its dynamical properties are investigated. Various properties of the oscillator, like equilibria, bifurcations, and Lyapunov exponents (LEs),...

This paper investigates the relationship between synchronization, system dynamics, and bifurcation points. To investigate the synchronization of dynamical systems, first, two oscillators are considered. Then networks with different structures are generated. The Master Stability Function (MSF) and synchronization criterion are computed for various o...

This paper presents FFT bifurcation as a tool for investigating complex dynamics. Firstly, two well-known chaotic systems (Rössler and Lorenz) are discussed from the frequency viewpoint. Then, both discrete-time and continuous-time systems are studied. Various systems with different properties are discussed. In discrete-time systems, Logistic map a...

Obtaining the master stability function is a well-known approach to study the synchronization in networks of chaotic oscillators. This method considers a normalized coupling parameter which allows for a separation of network topology and local dynamics of the nodes. The present study aims to understand how the dynamics of oscillators affect the mas...

In this chapter, a chaotic oscillator is presented. Various dynamical behaviors of the oscillator are analyzed. The complex dynamics of the proposed oscillator are applied in a compression-encryption algorithm. Here, we propose an image compression-encryption method using compressed sensing and a chaotic oscillator. At first, the original image is...

This paper introduces a simple 1-dimensional map-based model of spiking neurons. During the past decades, dynamical models of neurons have been used to investigate the biology of human nervous systems. The models simulate experimental records of neurons’ voltages using difference or differential equations. Difference neuronal models have some advan...

Researchers are eager to understand how real-world systems respond to environmental parameter changes, especially in complex networks. In biological systems like genetic networks or ecological systems, the presence of agents in the networks has been proved. Hence, studying the tipping points and finding a way to manage them can prevent the extincti...

Multimedia data play an important role in our daily lives. The evolution of internet technologies means that multimedia data can easily participate amongst various users for specific purposes, in which multimedia data confidentiality and integrity have serious security issues. Chaos models play an important role in designing robust multimedia data...

Recently, chaotic dynamics and their properties have attracted lots of attention. Proposing new chaotic systems with unique features is a way of solving the mystery of generating chaotic dynamics. A 3D chaotic flow with infinite equilibria located on a line is proposed in this chapter. Dynamical behavior of the proposed system is investigated. The...

Designing novel mega-stable chaotic oscillators has been a hot topic of research lately. In the current paper, a two-dimensional mega-stable oscillator is presented. The oscillator has a vast amount of coexisting limit cycles that spread on a surface. The forced version of this system is a novel nonlinear oscillator with an immense number of coexis...

Recently, resilience has attracted much attention in the study of biological systems. The goal of this paper is to investigate the slowness in ischemic stroke patients. A Trier Social Stress Test (TSST) is used to reveal the slowness of the biological system. The slowness of dynamics is calculated for the Electrocardiogram (ECG) of healthy individu...

In this research, the ship power system is studied with a fractional-order approach. A 2-D model of a two-generator parallel-connected is considered. A chaotic attractor is observed for particular parameter values. The fractional-order form is calculated with the Adam–Bashforth–Moulton method. The chaotic response is identified even for the order 0...

Studying the dynamical behaviors of neuronal models may help in better understanding of real nervous system. In addition, it can help researchers to understand some specific phenomena in neuronal system. The thalamocortical network is made of neurons in the thalamus and cortex. In it, the memory function is consolidated in sleep by creating up and...

Recently, the evolution of people cooperation in the context of evolutionary games has attracted noticeable attention. In this regard, people’s assessment of their neighbor’s payoff affects the cooperation or defection decisions. Different decisions of each person can be a function of environment (e.g. cultural, climatic, and physical conditions)....

A chaotic system that can show multiscroll and megastable attractors is studied in this paper. Two cases of the system with periodic and quasi-periodic excitations are discussed. Various stabilities of the system determined by changing parameters and initial values are investigated for both cases. In Case-A of the proposed system, multiscroll attra...

In this paper, a multi-stable chaotic hyperjerk system with both self-excited and hidden attractors is proposed. Such a system is infrequent between dynamical systems. State-space, bifurcation, and Lyapunov exponent plots are presented to show the existence of chaotic dynamics. The fractional-order model of the system and its dynamical properties a...

We study the synchronization of coupled identical circulant and non-circulant oscillators using single variable and different multi-variable coupling schemes. We use the master stability function to determine conditions for synchronization, in particular the necessary coupling parameter that ensures a stable synchronization manifold. We show that f...

Recently, researchers showed that adding a stepwise control pulse to the Sprott C system (with two equilibrium points) can create a translational multi-butterfly attractor. In this research, a sinusoidal control pulse is added to a system with no equilibria. So, a non-autonomous chaotic system with no equilibria is designed and studied. The sinusoi...

Various chaotic systems have been studied recently. They can show many different dynamics and features. A memristive 4D chaotic oscillator with no equilibria, multistability, and hidden attractor is presented in this paper. Chaotic attractor of the proposed oscillator is discussed, and its dynamical behaviors are investigated. The oscillator does n...

Many dynamical systems, particularly biological ones, exhibit different regimes in which the dynamics of the system vary from one regime to another through a critical transition. These transitions are critical points (CPs). The CPs can be observed with a critical slowing down phenomenon in which the attractor gets fragile. Due to the importance of...

In this paper, we propose a guideline for plotting the bifurcation diagrams of chaotic systems. We discuss numerical and mathematical facts in order to obtain more accurate and more elegant bifurcation diagrams. The importance of transient time and the phenomena of critical slowing down are investigated. Some critical issues related to multistabili...

In this chapter, a new three-dimensional chaotic system with infinitely many equilibria located on a line is proposed. Investigation of dynamical properties of the new system shows its various complex dynamical behaviours. Circuit implementation verifies the feasibility of the system for engineering applications.

Critical slowing down is considered to be an important indicator for predicting critical transitions in dynamical systems. Researchers have used it prolifically in the fields of ecology, biology, sociology, and finance. When a system approaches a critical transition or a tipping point, it returns more slowly to its stable attractor under small pert...

In this paper, we investigate epileptic seizures with the help of bifurcations in the network of neurons. The bifurcations of these neurons are investigated in one-layer and multi-layer network with different coupling strength. Bifurcations of networks are studied in various aspects. Also, dynamical properties of different networks and the single n...

Coronavirus disease 2019 is a recent strong challenge for the world. In this paper, an epidemiology model is investigated as a model for the development of COVID-19. The propagation of COVID-19 through various sub-groups of society is studied. Some critical parameters, such as the background of mortality without considering the disease state and th...

Investigating the dynamical properties of mechanical systems has been an attractive topic recently. In this paper, the dynamical properties of an impact oscillator are studied. The impact oscillator is a non-autonomous system with possible chaotic attractors. The oscillator without external force has a stable equilibrium. Bifurcation analysis of th...

A new hyperchaotic system with fractional terms and fractional order derivatives is proposed in this paper. Simulations show that different attractors such as equilibrium point, limit cycle and hyperchaotic attractor can be generated by the system. Circuit of fractional order integrator is designed and it is used to implement the circuit of the pro...

Synchronization in complex networks is an evergreen subject with numerous applications in biological, social, and technological systems. We here study whether a transition from a single variable to multivariable coupling facilitates the emergence of synchronization in a network of circulant oscillators. We show that the network indeed has much bett...

The electrical activity of neurons depends on the physiological conditions in the nervous system. An electromagnetic field, for example, can significantly affect the dynamics of individual neural cells, and it also affects their collective dynamics. It is therefore of interest to study the neuronal dynamics under such an influence in various setups...

A rare three-dimensional chaotic system with all eigenvalues equal to zero is proposed, and its dynamical properties are investigated. The chaotic system has one equilibrium point at the origin. Numerical analysis shows that the equilibrium point is unstable. Bifurcation analysis of the system shows various dynamics in a period-doubling route to ch...

In this paper, some new three-dimensional chaotic systems are proposed. The special property of these autonomous systems is their identical eigenvalues. The systems are designed based on the general form of quadratic jerk systems with 10 terms, and some systems with stable equilibria. Using a systematic computer search, 12 simple chaotic systems wi...

A new three-dimensional chaotic flow is proposed in this paper. The system is the simplest chaotic flow that has a line of equilibria. The chaotic attractor of the system is very special with two slow and fast parts. In other words, the dynamic of the system is a combination of slow and fast states. The unique chaotic attractor of the system is inv...

This paper proposes a behavioral model for cells that shows their different dynamics from a high pluripotent stem cell to any distinct cell fate. The proposed model considers a cell as a black-box for a living system and tries to depict the presumed behaviors of the system. The model is a multistable iterated map with sensitive dependence on initia...

In this paper, a new four-dimensional chaotic flow is proposed. The system has a cyclic symmetry in its structure and shows a complicated, chaotic attractor. The dynamical properties of the system are investigated. The system shows multistability in an interval of its parameter. Fractional order model of the proposed system is discussed in various...

This paper proposes a new chaotic system with a specific attractor which is bounded in a sphere. The system is offered in the spherical coordinate. Dynamical properties of the system are investigated in this paper. The system shows multistability, and all of its attractors are inside or on the surface of the specific sphere. Bifurcation diagram of...

A new five-dimensional chaotic system with extreme multi-stability is introduced in this article. The mathematical model is established, and numerical simulations are done. This dynamical system complicates incident of extreme multi-stability. Most significantly, relied on the mathematical model, the recently proposed system has a curve of equilibr...

This paper aims to investigate critical slowing down indicators in different situations where the system’s parameters change. Variation of the bifurcation parameter is important since it allows finding bifurcation points. A system’s parameters can vary through different functions. In this paper, five cases of bifurcation parameter variation are con...

In this paper, bifurcations of a memristive neuron model are analyzed. The system shows different limit cycles and chaotic attractors by varying external current. The focus of this paper is finding bifurcation points of the system and predicting them using critical slowing down indicators. The system has different tipping points such as transition...

In this paper, the simplest chaotic oscillator with fractional-order-memristor component (SCOF) is proposed. Dynamical characteristics of the proposed chaotic oscillator are investigated both analytically and numerically. The results indicate that the proposed chaotic oscillator possesses novel dynamical characteristics: double-scroll chaotic attra...

In this paper, we announce a novel 4D chaotic system which belongs to the self-excited attractor and hidden attractor family depending on the parameter values. Lyapunov exponents, bifurcation diagram and bicoherence plot of the CAMO (Camouflage) chaotic system are investigated. Also, fractional-order model of the proposed CAMO system (FOCAMO) is de...

A memristor diode bridge chaotic circuit is proposed in this paper. The proposed oscillator has only one nonlinear element in the form of memristor. Dynamical properties of the proposed oscillator are investigated. The fractional order model of the oscillator is designed using Grünwald–Letnikov (GL) method. Bifurcation diagrams are plotted which sh...

Designing chaotic systems with specific features is a hot topic in nonlinear dynamics. In this study, a novel chaotic system is presented with a unique feature of crossing inside and outside of a cylinder repeatedly. This new system is thoroughly analyzed by the help of the bifurcation diagram, Lyapunov exponents’ spectrum, and entropy measurement....

In this paper, we propose a new model to describe variations in interpretation and perception of a simple sentence by different people. To show the understandability of a simple sentence in the prediction of future situations, the meaning of a sentence is modeled as a fuzzy if-then rule, and the fuzzy model is investigated in an iterative process....

In this paper, a new structure of chaotic systems is proposed. There are many examples of differential equations with analytic solutions. Chaotic systems cannot be studied with the classical methods. However, in this paper we show that a system that has a simple analytical solution can also have a strange attractor. The main goal of this paper is t...

The importance of coupling between neurons is confirmed that signal propagation and exchange between neurons depend on the biological function of synapse connection. There is a high demand for models to simulate this phenomenon comprehensively. In this paper, we introduce four models to describe different types of coupling, based on the type of syn...

In this paper a modified third order Wien bridge oscillator with fractional order memristor is proposed. Various dynamical properties of the proposed oscillator are investigated such as equilibrium points, Eigenvalues, Lyapunov exponents and bifurcation diagrams. The Lyapunov spectrum of the system for various values of fractional order is derived....

Modeling real dynamical systems is an important challenge in many areas of science. Extracting governing equations of systems from their time-series is a possible solution for such a challenge. In this paper, we use the sparse recovery and dictionary learning to extract governing equations of a system with parametric basis functions. In this algori...

In this paper, we introduce a novel integer-order memristor-modified Shinriki circuit (MMSC). We investigate the dynamic properties of the MMSC system and the existence of chaos is proved with positive largest Lyapunov exponent. Bifurcation plots are derived to analyze the parameter dependence of the MMSC system. The fractional-order model of the M...

In this chapter, we investigate two discrete systems with interesting dynamics and applications. Different dynamical properties of these systems are investigated. The first one is a one-dimensional chaotic map which can generate signals with normal distribution. Distributions made in this way, in addition to being very similar to the normal distrib...

Many studies have been done on different aspects of biped robots such as motion, path planning, control and stability. Dynamical properties of biped robot on a sloping surface such as equilibria and their stabilities, bifurcations and basin of attraction are investigated in this paper. Basin of attraction is an important property since it can deter...

We propose a modified Fitzhugh-Nagumo neuron (MFNN) model. Based on this model, an integer-order MFNN system (case A) and a fractional-order MFNN system (case B) were investigated. In the presence of electromagnetic induction and radiation, memductance and induction can show a variety of distributions. Fractional-order magnetic flux can then be con...

In this paper, a three dimensional chaotic system with special properties is investigated. The system has an unstable equilibrium and a self-excited chaotic attractor in some parameters. Bifurcation analysis of the system shows different dynamics such as periodic orbit, torus and chaos. Also the system has multistability with some symmetric coexist...

Detection of epileptic seizures is a major challenge of these days. There are lots of papers which pay their attention to this subject. Recently, some dynamical disease with attacks such as epilepsy are considered as a system in which critical slowing down can be seen before their attacks (seizure). Although there are not many researches on the pre...

Classical indicators of tipping points have limitations when they are applied to an ecological and a biological model. For example, they cannot correctly predict tipping points during a period-doubling route to chaos. To counter this limitation, we here try to modify four well-known indicators of tipping points, namely the autocorrelation function,...

In this paper, a new multi-character dynamical system is proposed. It has chaotic and hyper-chaotic attractors without any equilibrium, with a line of equilibria or with unstable equilibrium. It means that the proposed system can change its characteristic by varying its parameters. This system shows multi-stability between different attractors such...

In this paper we announce a novel chaotic system which can have self-excited or hidden attractor depending on the parameters. The system shows same Lyapunov exponents for both self-excited and hidden attractors. Fractional order model of the proposed novel chaotic system is derived and investigated. Bifurcation diagrams of the fractional order chao...

This paper investigates a three-dimensional autonomous chaotic flow without linear terms. Dynamical behavior of the proposed system is investigated through eigenvalue structures, phase portraits, bifurcation diagram, Lyapunov exponents and basin of attraction. For a suitable choice of the parameters, the proposed system can exhibit anti-monotonicit...

In this paper, we propose a fuzzy model predictive control method, which can be used in the control of highly nonlinear and complex systems, like chaotic ones. This method only uses the obtained time series of the system and does not require any prior knowledge about the system's equations. In our proposed method, a fuzzy model is created using a c...

In honor of his 75th birthday, we review the prominent works of Professor Julien Clinton Sprott in chaos and nonlinear dynamics. We categorize his works into three important groups. The first and most important group is identifying new dynamical systems with special properties. He has proposed different chaotic maps, flows, complex variable systems...

This paper mathematically investigates the process equation. The process equation is a one-dimensional map Ak+1 = Ak + gsin(Ak). It can show multistable attractors and various dynamics such as period doubling, unifurcation, chaos, bios, unstable windows and bio-periodic windows with respect to the changing of its control parameter, g. Different dyn...

The primary goal in this work is to develop a dynamical model capturing the influence of seasonal and latitudinal variations on the expression of Drosophila clock genes. To this end, we study a specific dynamical system with strange attractors that exhibit changes of Drosophila activity in a range of latitudes and across different seasons. Bifurcat...

Transitions from one dynamical regime to another one are observed in many complex systems, especially biological ones. It is possible that even a slight perturbation can cause such a transition. It is clear that this can happen to an object when it is close to a tipping point. There is a lot of interest in finding ways to recognize that a tipping p...

Perpetual Points (PPs) have been introduced as an interesting new topic in nonlinear dynamics, and there is a conjecture that these points can be used to find hidden attractors. This note demonstrates some examples where PPs cannot locate their hidden attractors.

This paper investigates the different behaviors of the process equation and parameters of their occurrences. The process equation is a multistable one dimensional map with nonlinear feedback and can show various behaviors such as period doubling route to chaos, bios, unstable windows and periodic windows. In this note, we focus on different behavio...

Perpetual points represent a new interesting topic in the literature of nonlinear dynamics. This paper introduces some chaotic flows with four different structural features from the viewpoint of fixed points and perpetual points.