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# Ising model simulations of a dynamic system at critical and non-critical temperatures. (A) Binary 128 6 128 lattices showing the configuration of spins after 2,000 timesteps at low temperature, T ~ 0 (left); critical temperature, T ~ T c (middle); and high temperature, T ~ 10 5 (right). At hot temperature the spins are randomly configured, at low temperature they are close to an entirely ordered state, and at critical temperature they have a fractal configuration. (B) Probability distribution of phase lock interval (PLI) between pairs of processes at critical (black line) and at hot temperature (red line) plotted on a log-log scale. The black dashed line represents a power law with slope a ~{ 1 : 5 . (C) Probability distribution of lability of global synchronization ( D 2 ) at critical temperature (black line) and at hot temperature (red dotted line); the black dashed line represents a power law with slope a ~{ 0 : 5 . For the cold Ising model the equilibrium state of the system is a monolithic lattice with either all spins up or down, resulting in an entirely static system for which the PLI distribution is a Dirac Delta peak at the duration of the time series. The key point is that the probability distributions of both duration of pairwise synchronization, indexed by the phase lock interval, and lability of global synchronization, show power law behaviour for the 2D Ising model specifically at critical temperature. doi:10.1371/journal.pcbi.1000314.g001

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Self-organized criticality is an attractive model for human brain dynamics, but there has been little direct evidence for its existence in large-scale systems measured by neuroimaging. In general, critical systems are associated with fractal or power law scaling, long-range correlations in space and time, and rapid reconfiguration in response to ex...

## Contexts in source publication

**Context 1**

... dynamics are recognized as typical of many different physical systems including piles of rice or sand, earthquakes and mountain avalanches. Dynamic systems in a critical state will generally demonstrate scale-invariant organization in space and/ or time, meaning that there will be similar fluctuations occurring at all time and length scales in the system. In other words, there is no characteristic scale to critical dynamics, which will be optimally described by scale-invariant or fractal metrics. Thus, power law or fractal scaling has been widely accepted as a typical empirical signature of non-equilibrium systems in a self-organized critical state [1], although the existence of power law scaling does not by itself prove that the system is self-organized critical (SOC). For example, turbulence is a conceptually distinct class of dynamics, which is also characterized by self-similar or scale-invariant energy cascades, that can be empirically disambiguated from criticality [2,3]. The existence of power laws for the spatial and temporal statistics of critical systems is compatible with the related observations that the dynamics of individual units or components of such systems will show long-range correlations in space and time, and change in state of a single unit can rapidly trigger macroscopic reconfiguration of the system. Many of these phenomena can be studied using computational models of dynamic systems such as the Ising model of magnetization (see Figure 1) and the Kuramoto model of phase coupled oscillators (see Figure 2). In both these models, the dynamics can be controlled by continuous manipulation of a single parameter. For the Ising model, this control parameter is the temperature; whereas for the Kuramoto model it is the strength of coupling between oscillators. In both cases, as the control parameter is gradually increased (or decreased), the dynamics of the systems will pass through a phase transition, from an ordered to a random state (or vice versa), at which point the emergence of power law scaling and other fractal phenomena will be observed at the so-called critical value of the control parameter. Self-organized critical systems differ from these computational models in the sense that they are not driven to the cusp of a phase transition by external manipulation of an control parameter but instead spontaneously evolve to exist dynamically at that point. Self-organized criticality is an intuitively attractive model for functionally relevant brain dynamics [4–7]. Many cognitive and behavioral states, including perception, memory and action, have been described as the emergent properties of coherent or phase- locked oscillation in transient neuronal ensembles [8–11]. Critical dynamics of such neurophysiological systems would be expected to optimize their capacity for information transfer and storage, and would be compatible with their rapid reconfiguration in response to changing environmental contingencies, conferring an adaptive ability to switch quickly between behavioral states [12]. In support of the criticality model for brain dynamics, there is already considerable evidence for fractal or power law scaling of anatomically localized neurophysiological processes - including spike frequency, synaptic transmitter release, endogenous EEG and fMRI oscillations [13–15] - measured on a wide range of spatial and time scales. However, there have been fewer direct demonstrations of critical dynamics of anatomically distributed neurophysiological systems . Beggs, Plenz and colleagues [16–18] have provided empirical evidence of criticality for neuronal network dynamics, represented by a power law probability distribution for the number of electrodes simultaneously recording spike activity in multielectrode array recordings of cortical slices, consistent with the fairly frequent occurrence of neuronal ‘‘avalanches’’. At the much larger spatial scale of human magnetoencephalography (MEG), the topology of small-world human brain functional networks was found to be self-similar over a range of frequency scales, and the network’s topology at each scale was consistent with dynamics close to the critical point of transition from macroscopically chaotic to ordered states [12]. Here we provide more direct evidence for critical dynamics of human brain functional networks measured using both functional magnetic resonance imaging (fMRI) and MEG. We focused on two measures of the phase synchronization between component processes of a dynamic system (which are defined more formally later): the phase lock interval (PLI) and the lability of global synchronization. The phase lock interval is simply the length of time that a pair of bandpass filtered neurophysiological signals, simultaneously recorded from two different MEG sensors or two different brain regions in fMRI, are in phase synchronization with each other. Thus it is a measure of functional coupling between an arbitrary pair of signals in the system. The lability of global synchronization is a measure of how extensively the total number of phase locked pairs of signals in the whole system can change over time. A globally labile system will experience occasional massive coordinated changes in coupling between many of its component elements. In this sense, global lability is informally analogous to the measure of neuronal ‘‘avalanches’’ introduced by Beggs & Plenz (2003) to describe simultaneous spiking of large numbers of cells in a multielectrode array measurement of spontaneous neuronal activity. In order to calibrate the behavior of these two synchronization metrics in relation to unquestionably critical dynamics, we first applied them to analysis of the Ising and Kuramoto models as their control parameters were manipulated systematically. These preliminary analyses of two mechanistically distinct computational models demonstrated that the probability distributions of both synchronization metrics followed a power law specifically when the models were in a critical state. This suggested that power law scaling of network synchronization was indicative of critical dynamics regardless of differences in the mechanistic interactions between components in the two models. On this basis, we proceeded to investigate the behavior of these synchronization metrics in neurophysiological data recorded from healthy human volunteers using functional MRI and MEG. Scale-dependent phase synchronization. To calculate ...

**Context 2**

... average s 2 ~ C ij 2 provides a direct measure of the significance of this phase difference estimate. To see this, we note that 2 lim D t ? ? C ij ~ 0 for independent phases and 1 when there is complete phase locking. In fact s 2 is formally equivalent to the definition of classical coherence, with Fourier coefficients replaced by wavelet coefficients. We also note that C ij is very similar to the standard phase synchronization index gamma described by Pikovsky et al. [23]. Specifically, gamma is equivalent to S C ij T , the modulus of the time-windowed moving average of our metric C ij , as defined in Equation 1. However, we decided to perform the averaging in a slightly different way, as shown in Equation 2, such that phase vectors with larger amplitude were given greater weight in the average. This refinement of the standard gamma metric improves its robustness against phase interference inherent in the rather noisy experimental data. Intervals of phase-locking, or phase synchronization, can be defined as periods when D w ij ð t Þ is smaller than some arbitrary value. Here we will define the two processes as phase-locked or synchronized when { p = 4 v D w ij ð t Þ v p = 4 , and the duration of phase locking, or phase locked interval, is the length of time for which this condition holds true. The threshold value of j p = 4 j was chosen because it represents the mid-point between exact synchronization D w ð t Þ ~ 0 and complete independence D w ij t ~ p = 2 or { p = 2 . (Note that phase differences p = 2 v j D w j v p denote various degrees of anti -correlation rather than independence.) Additionally we require s 2 ij w 1 = 2 , limiting our analysis to phase difference estimates above this level of significance. Global lability of synchronization. Given estimates of the phase difference between each pair of signals in the system, it is then possible to count the number of pairs of signals that are phase-locked at any point in time: This provides a global measure of the extent of synchronization in the system. We can also calculate the difference in the number of synchronized pairs at two points in time: choosing a value of D t larger than the window size L win used to calculate the phase difference. This provides a measure of the lability of global synchronization of the system. Large values of D 2 ð t , D t Þ indicate extensive change in global synchronization. The Ising model. The Ising model [24] was originally defined as a 1D model of ferromagnetism but has since been extended in generality to two and higher dimensions [25]. Recently it has also become widely used as a paradigmatic example of critical dynamics in a relatively simple system [26]. We defined a 2D Ising model operationally as follows. In a square f L | L g lattice, each one of i ~ 1,2,3, . . . , L sites was associated with a variable or ‘‘spin’’, s i , with one of two possible values, + 1 (an up spin) or 2 1 (a down spin). Thus any particular configuration of the lattice was completely specified by the set of variables f s 1 , s 2 , s 3 , . . . , s g . The energy of the system is given by where J is the coupling constant and the sum of j runs over the nearest neighbors nn ð i Þ of a given site i . At a given point in time, a spin can flip from one possible state to another if it is energetically favorable but also if it is not, with the probability P ~ e , where k is Boltzmann’s constant and T is the temperature (analogous to an actual physical system). The simulation was implemented with the Metropolis Monte Carlo algorithm solving for a given temperature T . In the case of the 2D Ising model the critical temperature T c is defined [27] by the equation or equivalently T c ~ 2 : 269 if we choose units such that J ~ k ~ 1 without loss of generality. We instantiated this model in a {96 6 96} lattice at three different temperatures: T ~ 0 (cold), T ~ T c (critical) and T ~ 10 5 (hot). Our objective was to estimate instantaneous phase differences between each pair of signals (Equation 3), and the lability of global synchronization (Equation 5), in these simulations to provide a point of reference for comparable analysis of neurophysiological data. To produce time series that were continuously variable in the range [ 2 64,64], rather than binary, the magnetization was averaged over local neighborhoods or square {8 6 8} sub-lattices at each time point, resulting in 144 continuous time series. Each simulation was initiated with the spins in a random configuration and iterated for 12,192 time steps. At low temperatures it will take the system some time to reach its equilibrium state and we therefore restricted our analysis to the final 8,192 timepoints of each simulation. In the simulated data from the 2D Ising model at critical temperature, we found that the probability distributions for both the phase-lock interval (PLI) and global lability ( D 2 ) demonstrated power law scaling specifically when the system was at critical temperature; see Figure 1. The Kuramoto model. The 2D Ising model is one of the simplest computational models available for studying critical dynamics, which is its main advantage. However, the physical mechanism on which it is based, magnetic coupling of neighbouring spins in a ferromagnetic material, and the extreme simplicity of its components, binary spins, may seem to be implausibly related to the components and mechanisms of brain networks. We therefore also implemented the Kuramoto model as an alternative, independent model of critical dynamics. This seemed a natural choice since our measures of network dynamics are based on phase synchronization, and the Kuramoto model describes the phase evolution of its elements explicitly. It is also a parsimoniously simple system, yet able to produce a number of surprisingly complex phenomena. In particular, it will undergo a second order phase transition when the coupling parameter is in the vicinity of its critical value K c , analogous to the critical temperature in the Ising model. The Kuramoto model has been widely used to study synchronization phenomena in complex dynamical systems [28] arising in many different contexts ranging from physics to biology. For example, it has been applied to the neurophysiological problem of stimulus integration in sensory processing in neural networks [8,29] and also to the study of intermittent dynamics in EEG data [30]. In the Kuramoto model, the system is comprised of N limit- cycle oscillators each of which has its own natural frequency v i , and is also coupled to all other oscillators in the system through a periodic function of the pairwise phase difference h j { h i , such that the differential equation for the evolution of the phase of a given oscillator h i is: where K denotes coupling strength. The distribution of natural frequencies g ð v Þ can be chosen freely but is usually limited to being unimodal and symmetric about its mean v . Moreover, without loss of generality, we can transform the coordinate system into a comoving frame, rotating at v , such that the effective mean frequency becomes v ~ 0 . For our simulations, we selected a set of 44 normally distributed frequencies with zero mean and unit variance g ð v Þ ~ N ð 0,1 Þ . As demonstrated analytically by Kuramoto [31], the critical coupling exponent K c does not depend on the exact shape of g ð v Þ , but is solely a function of the probability density at the central frequency g ð 0 Þ : With g v ~ 0,1 this would formally give K c ~ 8 = p ~ 1 : 596 , but since we used a discrete frequency distribution rather than a continuous one, we calculate the probability density independently using a smoothing kernel approach. This gives a slightly different result, depending on the exact set of natural frequencies v i . It is convenient to introduce a global order parameter r as the modulus of the complex mean over all phase vectors where y is the mean phase. With this definition Equation 8 can be rewritten in terms of coupling to the mean field : In this form, the equation for the phase evolution in the model becomes more intuitive. In particular, under the assumption that the mean field reaches a stationary equilibrium in the limit t ? ? , then r and y become invariant and the differential equations decouple completely. This is how Kuramoto initially solved the model analytically. However, we are not interested in the model when it is in a quasi-stationary state but rather when it is in an unstable or metastable state, which is the case when the coupling strength is at the critical value K c . This can be seen in Figure 2, which illustrates the rapid change of the system states when the coupling strength exceeds K c . The point of critical coupling strength is marked by the greatest fluctuation in the number of synchronized pairs, and the greatest range of Kr , the strength of effective coupling to the mean field (see Equation 11). Consequently the oscillators whose effective frequencies lie within this range experience intermittent periods of strong and weak driving by the mean field, pushing them in and out of synchronization, resulting in a chaotic system. The evolution of each individual oscillator is thus dynamically equivalent to a circle-map oscillator, a prototypical chaotic system [32]. To generate time series from the Kuramoto model in critical and non-critical states, we simulated the phase evolution of a set of 44 coupled oscillators (with natural frequencies specified as described above) and solved the set of 44 coupled evolution equations (Equation 8) numerically using ODE solvers which distinguish automatically between stiff and non-stiff problems [33,34]. Each simulation ran for 10 5 time steps, which were selected to be sufficiently small to sample the highest frequencies in the model accurately with at least 8 values per cycle. Two sets of time series were produced: one with the coupling parameter set at its critical value K c and one with K ~ 0 , i.e. free ...

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... This suggests that living creatures embody critical internal representations that unfold across a multiplicity of temporal scales. In humans, this is reflected for instance in the temporal frequency perception of natural scenes [148] and in brain synchronization metrics [149]. ...

We describe a chain of unidirectionally coupled adaptive excitable elements slowly driven by a stochastic process from one end and open at the other end, as a minimal toy model of unresolved irreducible uncertainty in a system performing inference through a hierarchical model. Threshold potentials adapt slowly to ensure sensitivity without being wasteful. Activity and energy are released as intermittent avalanches of pulses with a discrete scaling distribution largely independent of the exogenous input form. Subthreshold activities and threshold potentials exhibit Lorentzian temporal spectra, with a power-law range determined by position in the chain. Subthreshold bistability closely resembles empirical measurements of intracellular membrane potential. We suggest that critical cortical cascades emerge from a trade-off between metabolic power consumption and performance requirements in a critical world, and that the temporal scaling patterns of brain electrophysiological recordings ensue from weighted linear combinations of subthreshold activities and pulses from different hierarchy levels.

... Working with non-stationary dynamics provides a richer understanding of certain notions commonly associated with brain activity. For example, criticality is commonly associated with the ability to transit between random and ordered behaviour [49]. In our approach, this is associated with low criticality values. ...

The self-organising global dynamics underlying brain states emerge from complex recursive nonlinear interactions between interconnected brain regions. Until now, most efforts of capturing the causal mechanistic generating principles have supposed underlying stationarity, being unable to describe the non-stationarity of brain dynamics, i.e. time-dependent changes. Here, we present a novel framework able to characterise brain states with high specificity, precisely by modelling the time-dependent dynamics. Through describing a topological structure associated to the brain state at each moment in time (its attractor or ‘information structure’), we are able to classify different brain states by using the statistics across time of these structures hitherto hidden in the neuroimaging dynamics. Proving the strong potential of this framework, we were able to classify resting-state BOLD fMRI signals from two classes of post-comatose patients (minimally conscious state and unresponsive wakefulness syndrome) compared with healthy controls with very high precision.

... This type of learning is an essential concept for building neural networks capable of self-adaptation and possibly takes place in the human brain. 23 Also it is important to note that a self-adaptive neural network was recently created 21 by using cobalt atoms on a semiconductor black phosphorus substrate. 22 We aimed at creating a theoretical model of a neural network that could be simply investigated numerically, so that the phenomena of the edge-of-chaos learning and the self-adaptation could be studied. ...

... 30 This principle is spread widely in natural science, 31 especially in biology. 23 Also, it is actively discussed in the context of the implementation of neural networks, 32 . 33 The model proposed makes it possible to investigate the phenomenon of self-organized criticality both numerically and analytically in a framework of a simple quantum mechanical problem. ...

We consider a model of an artificial neural network based on quantum-mechanical particles in $W$ potential. These particles play the role of neurons in our model. To simulate such a quantum-mechanical system the Monte-Carlo integration method is used. A form of the self-potential of a particle as well as two interaction potentials (exciting and inhibiting) are proposed. Examples of simplest logical elements (such as AND, OR and NOT) are shown. Further we show an implementation of the simplest convolutional network in framework of our model.

... where coupling parameter J i j captures the interaction between neighboring neurons i and j. This formulation is equivalent to the well-known Ising model with no external field, which has been extensively used to model experimentally observed neural activity (Kitzbichler, Smith, Christensen, & Bullmore, 2009;Schneidman, Berry, Segev, & Bialek, 2006). We updated neurons in the network according to the standard procedure for the 2D Ising model (Yeomans, 2010), flipping the binary state of each neuron i from σ i (t) to σ i (t + 1) with probability ...

... Transition. The 2D Ising model has been demonstrated as a maximum entropy network model with near-critical dynamics that reproduces multiple features observed in brain dynamics (Fraiman, Balenzuela, Foss, & Chialvo, 2009;Kitzbichler et al., 2009). In particular, there exists a critical temperature, T c , that separates two phases of dynamics: subcritical T < T c where progressively smaller T produce larger clusters of synchronized neurons as illustrated in Figure 1D, (left), and supercritical T > T c where progressively larger T produce increasingly decoupled random neuron activity, shown in Figure 1D, (right). ...

Astrocytes are nonneuronal brain cells that were recently shown to actively communicate with neurons and are implicated in memory, learning, and regulation of cognitive states. Interestingly, these information processing functions are also closely linked to the brain's ability to self-organize at a critical phase transition. Investigating the mechanistic link between astrocytes and critical brain dynamics remains beyond the reach of cellular experiments, but it becomes increasingly approachable through computational studies. We developed a biologically plausible computational model of astrocytes to analyze how astrocyte calcium waves can respond to changes in underlying network dynamics. Our results suggest that astrocytes detect synaptic activity and signal directional changes in neuronal network dynamics using the frequency of their calcium waves. We show that this function may be facilitated by receptor scaling plasticity by enabling astrocytes to learn the approximate information content of input synaptic activity. This resulted in a computationally simple, information-theoretic model, which we demonstrate replicating the signaling functionality of the biophysical astrocyte model with receptor scaling. Our findings provide several experimentally testable hypotheses that offer insight into the regulatory role of astrocytes in brain information processing.

... The m'th order degree of a node n is given by k (m) n , which gives the number of hyperedges with size m that node n is a part of. The hyperdegree of node n is given by k n = {k (1) n , k (2) n , ..., k (M) n }, where M is the largest hyperedge size. For simplicity, we refer to hyperedges of sizes 2 and 3 as links and triangles respectively. ...

... Eq. (17) provides a low-dimensional description of the dynamics in terms of the hypergraph generative functions a (2) and a (3) . While the number of variables b(k) might still be large, Eq. (17) allows us to study the bifurcations and fixed points of the system. ...

... The factor of 2 in the definition of R (2) accounts for the fact that each triangle is counted twice in the calculation of R ...

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... One of the features of systems poised at the edge of criticality is power-law scalings. They have been observed across spatial dimensions-from individual neurones [28] to whole-brain networks derived from functional magnetic resonance imaging (fMRI) [29], as well as across temporal dimensions-both at the fast scale of EEG and magnetoencephalography (MEG) recordings [30,31] and at the slow scale of fMRI data [32]. It is further relevant to appreciate the properties that the system is endowed with close to criticality, as Figure 1. ...

In order to survive in a complex environment, the human brain relies on the ability to flexibly adapt ongoing behaviour according to intrinsic and extrinsic signals. This capability has been linked to specific whole-brain activity patterns whose relative stability (order) allows for consistent functioning, supported by sufficient intrinsic instability needed for optimal adaptability. The emergent, spontaneous balance between order and disorder in brain activity over spacetime underpins distinct brain states. For example, depression is characterized by excessively rigid, highly ordered states, while psychedelics can bring about more disordered, sometimes overly flexible states. Recent developments in systems, computational and theoretical neuroscience have started to make inroads into the characterization of such complex dynamics over space and time. Here, we review recent insights drawn from neuroimaging and whole-brain modelling motivating using mechanistic principles from dynamical system theory to study and characterize brain states. We show how different healthy and altered brain states are associated to characteristic spacetime dynamics which in turn may offer insights that in time can inspire new treatments for rebalancing brain states in disease.
This article is part of the theme issue ‘Emergent phenomena in complex physical and socio-technical systems: from cells to societies’.

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Significant advances have been made by identifying the levels of synchrony of the underlying dynamics of a given brain state. This research has demonstrated that non-conscious dynamics tend to be more synchronous than in conscious states, which are more asynchronous. Here we go beyond this dichotomy to demonstrate that different brain states are underpinned by dissociable spatiotemporal dynamics. We investigated human neuroimaging data from different brain states (resting state, meditation, deep sleep and disorders of consciousness after coma). The model-free approach was based on Kuramoto’s turbulence framework using coupled oscillators. This was extended by a measure of the information cascade across spatial scales. Complementarily, the model-based approach used exhaustive in silico perturbations of whole-brain models fitted to these measures. This allowed studying of the information encoding capabilities in given brain states. Overall, this framework demonstrates that elements from turbulence theory provide excellent tools for describing and differentiating between brain states.

... Indeed, neural systems seem to display features that are characteristic of systems at criticality. These include (i) the scaling invariance of neural avalanches 5,11 reported in diverse species 12,13 , through different imaging techniques 14 , and electro-physiological signals 15 ; (ii) the presence of long-range spatiotemporal correlations in the amplitude fluctuations of neural oscillations 16,17 , including the observation of 1/f power spectra from simultaneously recorded MEG/EEG signals 15 , fMRI 18 , and cognitive responses 19 ; and (iii) the increase of the correlation length with system size 17,20,21 . ...

The critical brain hypothesis states that biological neuronal networks, because of their structural and functional architecture, work near phase transitions for optimal response to internal and external inputs. Criticality thus provides optimal function and behavioral capabilities. We test this hypothesis by examining the influence of brain injury (strokes) on the criticality of neural dynamics estimated at the level of single participants using directly measured individual structural connectomes and whole-brain models. Lesions engender a sub-critical state that recovers over time in parallel with behavior. The improvement of criticality is associated with the re-modeling of specific white-matter connections. We show that personalized whole-brain dynamical models poised at criticality track neural dynamics, alteration post-stroke, and behavior at the level of single participants. The authors investigate the influence of brain injury (strokes) on the criticality of neural dynamics using directly measured connectomes and whole-brain models. They show that lesions engender a sub-critical state that recovers over time in parallel with behavior.

... critical brain hypothesis postulates that biological brains operate in a self-organized critical state [1][2][3][4][5]. While there was initially little evidence to support this hypothesis, subsequent advances in neuroscience have made it possible to observe the characteristic power-laws and avalanche dynamics as §sociated with critical transitions, first in cell cultures [6][7][8] and then in live animals and humans [9][10][11][12][13]. Although still controversial [14], the critical brain hypothesis is rapidly gaining support in mainstream neuroscience, fuelled by the growing amount of experimental evidence. ...

It has been postulated that the brain operates in a self-organized critical state that brings multiple benefits, such as optimal sensitivity to input. Thus far, self-organized criticality has typically been depicted as a one-dimensional process, where one parameter is tuned to a critical value. However, the number of adjustable parameters in the brain is vast, and hence critical states can be expected to occupy a high-dimensional manifold inside a high-dimensional parameter space. Here, we show that adaptation rules inspired by homeostatic plasticity drive a neuro-inspired network to drift on a critical manifold, where the system is poised between inactivity and persistent activity. During the drift, global network parameters continue to change while the system remains at criticality.

... Research pointing to the brain as being in a perpetual state of criticality on the "edge of chaos" between order and disorder is now gaining attention. It is said that criticality "would allow us to switch quickly between mental states in order to respond to changing environmental conditions" (Kitzbichler et al. 2009). ...

As I assume to begin with, animals with a high level of consciousness, are those beings which are more dependent on their materialistic ecological circumstances than those with less cognition. The most obvious support for this factual claim is the yet still unofficial unit of geological time named the Anthropocene Epoch demarcating human devastation of earthly resources, whereby there is no doubt which species on earth is the most materially dependent. Notwithstanding, we need to keep things quantitively in perspective. Of the 545.8 gigatons of biomass on Earth of which most is plants, animals make up 0.47% while humans only 0.01%, bacteria reigns supreme with 12.8% of total.