Synchronization of complex human networks

Synchronization in Coupled Laser Arrays with Correlated and Uncorrelated Disorder

The effect of quenched disorder in a many-body system is experimentally investigated in a controlled fashion. It is done by measuring the phase synchronization (i.e., mutual coherence) of 400 coupled lasers as a function of tunable disorder and coupling strengths. The results reveal that correlated disorder has a nontrivial effect on the decrease of phase synchronization, which depends on the ratio of the disorder correlation length over the average number of synchronized lasers. The experimental results are supported by numerical simulations and analytic derivations.

On the higher-order smallest ring-star network of Chialvo neurons under diffusive couplings

Network dynamical systems with higher-order interactions are a current trending topic, pervasive in many applied fields. However, our focus in this work is neurodynamics. We numerically study the dynamics of the smallest higher-order network of neurons arranged in a ring-star topology. The dynamics of each node in this network is governed by the Chialvo neuron map, and they interact via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through multi-body interactions. We deploy the higher-order coupling strength as the primary bifurcation parameter. We start by analyzing our model using standard tools from dynamical systems theory: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of disparate chaotic attractors. We also observe an interesting route to chaos from a fixed point via period-doubling and the appearance of cyclic quasiperiodic closed invariant curves. Furthermore, we numerically observe the existence of codimension-1 bifurcation points: saddle-node, period-doubling, and Neimark-Sacker. We also qualitatively study the typical phase portraits of the system, and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure, respectively. Finally, we study the synchronization behavior among the neurons using the cross correlation coefficient and the Kuramoto order parameter. We conjecture that unfolding these patterns and behaviors of the network model will help us identify different states of the nervous system, further aiding us in dealing with various neural diseases and nervous disorders.

Effects of individual practice on joint musical synchronization

Successful music-making requires precise sensorimotor synchronization, both in individual (solo) and joint (ensemble) social settings. We investigated how individual practice synchronizing with a temporally regular melody (Solo conditions) influences subsequent synchronization between two partners (Joint conditions). Musically trained adults practiced producing a melody by tapping on a keypad; each tap generated the next tone in the melody. First, the pairs synchronized their melody productions with their partner in a baseline Joint synchronization task. Then each partner separately synchronized their melody with a computer-generated recording of the partner's melody in a Solo intervention condition that presented either Normal (temporally regular) auditory feedback or delayed feedback (by 30-70 ms) in occasional (25%) randomly placed tone positions. Then the pairs synchronized again with their partner in a Joint condition. Next, they performed the second Solo condition (normal or delayed auditory feedback) followed again by the Joint condition. Joint synchronization performance was modeled with a delay-coupled oscillator model to assess the coupling strength between partners. Absolute asynchronies in the Solo Intervention tasks were greater in the Delayed feedback condition than in the Normal feedback condition. Model estimates yielded larger coupling values between partners in Joint conditions that followed the Solo Normal feedback than the Solo Delayed feedback. Notably, the asynchronies were smaller in the Joint conditions than in the Solo conditions. These findings indicate that coupled interactions in settings of two or more performers can be improved by individual synchronization practice.

Revealing the mechanism and function underlying pairwise temporal coupling in collective motion

Coordinated motion in animal groups has predominantly been studied with a focus on spatial interactions, such as how individuals position and orient themselves relative to one another. Temporal aspects have, by contrast, received much less attention. Here, by studying pairwise interactions in juvenile zebrafish (Danio rerio)-including using immersive volumetric virtual reality (VR) with which we can directly test models of social interactions in situ-we reveal that there exists a rhythmic out-of-phase (i.e., an alternating) temporal coordination dynamic. We find that reciprocal (bi-directional) feedback is both necessary and sufficient to explain this emergent coupling. Beyond a mechanistic understanding, we find, both from VR experiments and analysis of freely swimming pairs, that temporal coordination considerably improves spatial responsiveness, such as to changes in the direction of motion of a partner. Our findings highlight the synergistic role of spatial and temporal coupling in facilitating effective communication between individuals on the move.

Disparity-driven heterogeneous nucleation in finite-size adaptive networks

Phase transitions are crucial in shaping the collective dynamics of a broad spectrum of natural systems across disciplines. Here, we report two distinct heterogeneous nucleation facilitating single step and multistep phase transitions to global synchronization in a finite-size adaptive network due to the trade off between time scale adaptation and coupling strength disparities. Specifically, small intracluster nucleations coalesce either at the population interface or within the populations resulting in the two distinct phase transitions depending on the degree of the disparities. We find that the coupling strength disparity largely controls the nature of phase transition in the phase diagram irrespective of the adaptation disparity. We provide a mesoscopic description for the cluster dynamics using the collective coordinates approach that brilliantly captures the multicluster dynamics among the populations leading to distinct phase transitions. Further, we also deduce the upper bound for the coupling strength for the existence of two intraclusters explicitly in terms of adaptation and coupling strength disparities. These insights may have implications across domains ranging from neurological disorders to segregation dynamics in social networks.

Social and nonlinear dynamics unite: musical group synchrony

Synchronization, the human tendency to align behaviors in time with others, is necessary for many survival skills. The ability to synchronize actions with rhythmic (predictable) sound patterns is especially well developed in music making. Recent models of synchrony in musical ensembles rely on pairwise comparisons between group members. This pairwise approach to synchrony has hampered theory development, given current findings from social dynamics indicating shifts in members' influence within larger groups. We draw on social theory and nonlinear dynamics to argue that emergent properties and novel roles arise in musical group synchrony that differ from individual or pairwise behaviors. This transformational shift in defining synchrony sheds light on successful outcomes as well as on disruptions that cause negative behavioral outcomes.

Synchronization in simplicial complexes of memristive Rulkov neurons

Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.

Using compartmental models and Particle Swarm Optimization to assess Dengue basic reproduction number R 0 for the Republic of Panama in the 1999-2022 period

Nowadays, the ability to make data-driven decisions in public health is of utmost importance. To achieve this, it is necessary for modelers to comprehend the impact of models on the future state of healthcare systems. Compartmental models are a valuable tool for making informed epidemiological decisions, and the proper parameterization of these models is crucial for analyzing epidemiological events. This work evaluated the use of compartmental models in conjunction with Particle Swarm Optimization (PSO) to determine optimal solutions and understand the dynamics of Dengue epidemics. The focus was on calculating and evaluating the rate of case reproduction,R 0 , for the Republic of Panama. Three compartmental models were compared: Susceptible-Infected-Recovered (SIR), Susceptible-Exposed-Infected-Recovered (SEIR), and Susceptible-Infected-Recovered Human-Susceptible-Infected Vector (SIR Human-SI Vector, SIR-SI). The models were informed by demographic data and Dengue incidence in the Republic of Panama between 1999 and 2022, and the susceptible population was analyzed. The SIR, SEIR, and SIR-SI models successfully providedR 0 estimates ranging from 1.09 to 1.74. This study provides, to the best of our understanding, the first calculation ofR 0 for Dengue outbreaks in the Republic of Panama.

Notes on resonant and synchronized states in complex networks

Synchronization and resonance on networks are some of the most remarkable collective dynamical phenomena. The network topology, or the nature and distribution of the connections within an ensemble of coupled oscillators, plays a crucial role in shaping the local and global evolution of the two phenomena. This article further explores this relationship within a compact mathematical framework and provides new contributions on certain pivotal issues, including a closed bound for the average synchronization time in arbitrary topologies; new evidences of the effect of the coupling strength on this time; exact closed expressions for the resonance frequencies in terms of the eigenvalues of the Laplacian matrix; a measure of the effectiveness of an influencer node's impact on the network; and, finally, a discussion on the existence of a resonant synchronized state. Some properties of the solution of the linear swing equation are also discussed within the same setting. Numerical experiments conducted on two distinct real networks-a social network and a power grid-illustrate the significance of these results and shed light on intriguing aspects of how these processes can be interpreted within networks of this kind.

Adaptive fixed-time output synchronization for complex dynamical networks with multi-weights

This paper addresses fixed-time output synchronization problems for two types of complex dynamical networks with multi-weights (CDNMWs) by using two types of adaptive control methods. Firstly, complex dynamical networks with multiple state and output couplings are respectively presented. Secondly, several fixed-time output synchronization criteria for these two networks are formulated based on Lyapunov functional and inequality techniques. Thirdly, by employing two types of adaptive control methods, fixed-time output synchronization issues of these two networks are dealt with. At last, the analytical results are verified by two numerical simulations.

Interpersonal sensorimotor communication shapes intrapersonal coordination in a musical ensemble

Social behaviors rely on the coordination of multiple effectors within one's own body as well as between the interacting bodies. However, little is known about how coupling at the interpersonal level impacts coordination among body parts at the intrapersonal level, especially in ecological, complex, situations. Here, we perturbed interpersonal sensorimotor communication in violin players of an orchestra and investigated how this impacted musicians' intrapersonal movements coordination. More precisely, first section violinists were asked to turn their back to the conductor and to face the second section of violinists, who still faced the conductor. Motion capture of head and bow kinematics showed that altering the usual interpersonal coupling scheme increased intrapersonal coordination. Our perturbation also induced smaller yet more complex head movements, which spanned multiple, faster timescales that closely matched the metrical levels of the musical score. Importantly, perturbation differentially increased intrapersonal coordination across these timescales. We interpret this behavioral shift as a sensorimotor strategy that exploits periodical movements to effectively tune sensory processing in time and allows coping with the disruption in the interpersonal coupling scheme. As such, head movements, which are usually deemed to fulfill communicative functions, may possibly be adapted to help regulate own performance in time.

Chiral States in Coupled-Lasers Lattice by On-Site Complex Potential

The ability to control the chirality of physical devices is of great scientific and technological importance, from investigations of topologically protected edge states in condensed matter systems to wavefront engineering, isolation, and unidirectional communication. When dealing with large networks of oscillators, the control over the chirality of the bulk states becomes significantly more complicated and requires complex apparatus for generating asymmetric coupling or artificial gauge fields. Here we present a new approach for a precise control over the chirality of the bulk state of a triangular array of hundreds of symmetrically coupled lasers, by introducing a weak non-Hermitian complex potential, requiring only local on-site control of loss and frequency. In the unperturbed network, lasing supermodes with opposite chirality (staggered vortex and staggered antivortex) are equally probable. We show that by tuning the complex potential to an exceptional point, a nearly pure chiral lasing supermode is achieved. While our approach is applicable to any oscillators network, we demonstrate how the inherent nonlinearity of the lasers effectively pulls the network to the exceptional point, making the chirality extremely resilient against noise and imperfections.

Interpersonal synchronization of movement intermittency

Most animal species group together and coordinate their behavior in quite sophisticated manners for mating, hunting, or defense purposes. In humans, coordination at a macroscopic level (the pacing of movements) is evident both in daily life (e.g., walking) and skilled (e.g., music and dance) behaviors. By examining the fine structure of movement, we here show that interpersonal coordination is established also at a microscopic – submovement – level. Natural movements appear as marked by recurrent (2–3 Hz) speed breaks, i.e., submovements, that are traditionally considered the result of intermittency in (visuo)motor feedback-based control. In a series of interpersonal coordination tasks, we show that submovements produced by interacting partners are not independent but alternate tightly over time, reflecting online mutual adaptation. These findings unveil a potential core mechanism for behavioral coordination that is based on between-persons synchronization of the intrinsic dynamics of action-perception cycles.

•

Movements show intermittent speed pulses occurring at 2–3 Hz, called submovements

•

Submovements are actively coordinated in counter-phase by interacting partners

•

Submovements coordination depends on spatial alignment but not movement congruency

•

Behavioral coordination occurs both at macro- and microscopic movement scales

Complex Networks and the b-Value Relationship Using the Degree Probability Distribution: The Case of Three Mega-Earthquakes in Chile in the Last Decade

Studies from complex networks have increased in recent years, and different applications have been utilized in geophysics. Seismicity represents a complex and dynamic system that has open questions related to earthquake occurrence. In this work, we carry out an analysis to understand the physical interpretation of two metrics of complex systems: the slope of the probability distribution of connectivity (γ) and the betweenness centrality (BC). To conduct this study, we use seismic datasets recorded from three large earthquakes that occurred in Chile: the Mw8.2 Iquique earthquake (2014), the Mw8.4 Illapel earthquake (2015) and the Mw8.8 Cauquenes earthquake (2010). We find a linear relationship between the b−value and the γ value, with an interesting finding about the ratio between the b−value and γ that gives a value of ∼0.4. We also explore a possible physical meaning of the BC. As a first result, we find that the behaviour of this metric is not the same for the three large earthquakes, and it seems that this metric is not related to the b−value and coupling of the zone. We present the first results about the physical meaning of metrics from complex networks in seismicity. These first results are promising, and we hope to be able to carry out further analyses to understand the physics that these complex network parameters represent in a seismic system.

Temporal Coordination in Piano Duet Networked Music Performance (NMP): Interactions Between Acoustic Transmission Latency and Musical Role Asymmetries

Today’s audio, visual, and internet technologies allow people to interact despite physical distances, for casual conversation, group workouts, or musical performance. Musical ensemble performance is unique because interaction integrity critically depends on the timing between each performer’s actions and when their acoustic outcomes arrive. Acoustic transmission latency (ATL) between players is substantially longer for networked music performance (NMP) compared to traditional in-person spaces where musicians can easily adapt. Previous work has shown that longer ATLs slow the average tempo in ensemble performance, and that asymmetric co-actor roles and empathy-related traits affect coordination patterns in joint action. Thus, we are interested in how musicians collectively adapt to a given latency and how such adaptation patterns vary with their task-related and person-related asymmetries. Here, we examined how two pianists performed duets while hearing each other’s auditory outcomes with an ATL of 10, 20, or 40 ms. To test the hypotheses regarding task-related asymmetries, we designed duets such that pianists had: (1) a starting or joining role and (2) a similar or dissimilar musical part compared to their co-performer, with respect to pitch range and melodic contour. Results replicated previous clapping-duet findings showing that longer ATLs are associated with greater temporal asynchrony between partners and increased average tempo slowing. While co-performer asynchronies were not affected by performer role or part similarity, at the longer ATLs starting performers displayed slower tempos and smaller tempo variability than joining performers. This asymmetry of stability vs. flexibility between starters and joiners may sustain coordination, consistent with recent joint action findings. Our data also suggest that relative independence in musical parts may mitigate ATL-related challenges. Additionally, there may be a relationship between co-performer differences in empathy-related personality traits such as locus of control and coordination during performance under the influence of ATL. Incorporating the emergent coordinative dynamics between performers could help further innovation of music technologies and composition techniques for NMP.

A metastable attractor model of self-other integration (MEAMSO) in rhythmic synchronization

Human interaction is often accompanied by synchronized bodily rhythms. Such synchronization may emerge spontaneously as when a crowd's applause turns into a steady beat, be encouraged as in nursery rhymes, or be intentional as in the case of playing music together. The latter has been extensively studied using joint finger-tapping paradigms as a simplified version of rhythmic interpersonal synchronization. A key finding is that synchronization in such cases is multifaceted, with synchronized behaviour resting upon different synchronization strategies such as mutual adaptation, leading-following and leading-leading. However, there are multiple open questions regarding the mechanism behind these strategies and how they develop dynamically over time. Here, we propose a metastable attractor model of self-other integration (MEAMSO). This model conceptualizes dyadic rhythmic interpersonal synchronization as a process of integrating and segregating signals of self and other. Perceived sounds are continuously evaluated as either being attributed to self-produced or other-produced actions. The model entails a metastable system with two particular attractor states: one where an individual maintains two separate predictive models for self- and other-produced actions, and the other where these two predictive models integrate into one. The MEAMSO explains the three known synchronization strategies and makes testable predictions about the dynamics of interpersonal synchronization both in behaviour and the brain. This article is part of the theme issue 'Synchrony and rhythm interaction: from the brain to behavioural ecology'.

Dynamics of coupled Kuramoto oscillators with distributed delays

This paper studies the effects of two different types of distributed-delay coupling in the system of two mutually coupled Kuramoto oscillators: one where the delay distribution is considered inside the coupling function and the other where the distribution enters outside the coupling function. In both cases, the existence and stability of phase-locked solutions is analyzed for uniform and gamma distribution kernels. The results show that while having the distribution inside the coupling function only changes parameter regions where phase-locked solutions exist, when the distribution is taken outside the coupling function, it affects both the existence, as well as stability properties of in- and anti-phase states. For both distribution types, various branches of phase-locked solutions are computed, and regions of their stability are identified for uniform, weak, and strong gamma distributions.

Spontaneous emergence of leadership patterns drives synchronization in complex human networks

Synchronization of human networks is fundamental in many aspects of human endeavour. Recently, much research effort has been spent on analyzing how motor coordination emerges in human groups (from rocking chairs to violin players) and how it is affected by coupling structure and strength. Here we uncover the spontaneous emergence of leadership (based on physical signaling during group interaction) as a crucial factor steering the occurrence of synchronization in complex human networks where individuals perform a joint motor task. In two experiments engaging participants in an arm movement synchronization task, in the physical world as well as in the digital world, we found that specific patterns of leadership emerged and increased synchronization performance. Precisely, three patterns were found, involving a subtle interaction between phase of the motion and amount of influence. Such patterns were independent of the presence or absence of physical interaction, and persisted across manipulated spatial configurations. Our results shed light on the mechanisms that drive coordination and leadership in human groups, and are consequential for the design of interactions with artificial agents, avatars or robots, where social roles can be determinant for a successful interaction.

One-way dependent clusters and stability of cluster synchronization in directed networks

Cluster synchronization in networks of coupled oscillators is the subject of broad interest from the scientific community, with applications ranging from neural to social and animal networks and technological systems. Most of these networks are directed, with flows of information or energy that propagate unidirectionally from given nodes to other nodes. Nevertheless, most of the work on cluster synchronization has focused on undirected networks. Here we characterize cluster synchronization in general directed networks. Our first observation is that, in directed networks, a cluster A of nodes might be one-way dependent on another cluster B: in this case, A may remain synchronized provided that B is stable, but the opposite does not hold. The main contribution of this paper is a method to transform the cluster stability problem in an irreducible form. In this way, we decompose the original problem into subproblems of the lowest dimension, which allows us to immediately detect inter-dependencies among clusters. We apply our analysis to two examples of interest, a human network of violin players executing a musical piece for which directed interactions may be either activated or deactivated by the musicians, and a multilayer neural network with directed layer-to-layer connections.

Mechanisms of cluster formation in networks with directed links differ from those in undirected networks. Lodi et al. propose a method to compute interdependencies among clusters of nodes in directed networks. They show that clusters can be one-way dependent, as found in social and neural networks.

Synchronization of gene expression across eukaryotic communities through chemical rhythms

The synchronization is a recurring phenomenon in neuroscience, ecology, human sciences, and biology. However, controlling synchronization in complex eukaryotic consortia on extended spatial-temporal scales remains a major challenge. Here, to address this issue we construct a minimal synthetic system that directly converts chemical signals into a coherent gene expression synchronized among eukaryotic communities through rate-dependent hysteresis. Guided by chemical rhythms, isolated colonies of yeast Saccharomyces cerevisiae oscillate in near-perfect synchrony despite the absence of intercellular coupling or intrinsic oscillations. Increased speed of chemical rhythms and incorporation of feedback in the system architecture can tune synchronization and precision of the cell responses in a growing cell collectives. This synchronization mechanism remain robust under stress in the two-strain consortia composed of toxin-sensitive and toxin-producing strains. The sensitive cells can maintain the spatial-temporal synchronization for extended periods under the rhythmic toxin dosages produced by killer cells. Our study provides a simple molecular framework for generating global coordination of eukaryotic gene expression through dynamic environment.

A Methodological Framework for Assessing Social Presence in Music Interactions in Virtual Reality

Virtual reality (VR) brings radical new possibilities to the empirical study of social music cognition and interaction. In the present article, we consider the role of VR as a research tool, based on its potential to create a sense of "social presence": the illusory feeling of being, and socially interacting, inside a virtual environment. This makes VR promising for bridging ecological validity ("research in the wild") and experimental control ("research in the lab") in empirical music research. A critical assumption however is the actual ability of VR to simulate real-life social interactions, either via human-embodied avatars or computer-controlled agents. The mediation of social musical interactions via VR is particularly challenging due to their embodied, complex, and emotionally delicate nature. In this article, we introduce a methodological framework to operationalize social presence by a combination of factors across interrelated layers, relating to the performance output, embodied co-regulation, and subjective experiences. This framework provides the basis for the proposal of a pragmatic approach to determine the level of social presence in virtual musical interactions, by comparing the outcomes across the multiple layers with the outcomes of corresponding real-life musical interactions. We applied and tested this pragmatic approach via a case-study of piano duet performances of the piece Piano Phase composed by Steve Reich. This case-study indicated that a piano duet performed in VR, in which the real-time interaction between pianists is mediated by embodied avatars, might lead to a strong feeling of social presence, as reflected in the measures of performance output, embodied co-regulation, and subjective experience. In contrast, although a piano duet in VR between an actual pianist and a computer-controlled agent led to a relatively successful performance output, it was inadequate in terms of both embodied co-regulation and subjective experience.

Discordant synchronization patterns on directed networks of identical phase oscillators with attractive and repulsive couplings

We study the collective dynamics of identical phase oscillators on globally coupled networks whose interactions are asymmetric and mediated by positive and negative couplings. We split the set of oscillators into two interconnected subpopulations. In this setup, oscillators belonging to the same group interact via symmetric couplings while the interaction between subpopulations occurs in an asymmetric fashion. By employing the dimensional reduction scheme of the Ott-Antonsen (OA) theory, we verify the existence of traveling wave and π-states, in addition to the classical fully synchronized and incoherent states. Bistability between all collective states is reported. Analytical results are generally in excellent agreement with simulations; for some parameters and initial conditions, however, we numerically detect chimera-like states which are not captured by the OA theory.

Stability of synchronization in simplicial complexes

Various systems in physics, biology, social sciences and engineering have been successfully modeled as networks of coupled dynamical systems, where the links describe pairwise interactions. This is, however, too strong a limitation, as recent studies have revealed that higher-order many-body interactions are present in social groups, ecosystems and in the human brain, and they actually affect the emergent dynamics of all these systems. Here, we introduce a general framework to study coupled dynamical systems accounting for the precise microscopic structure of their interactions at any possible order. We show that complete synchronization exists as an invariant solution, and give the necessary condition for it to be observed as a stable state. Moreover, in some relevant instances, such a necessary condition takes the form of a Master Stability Function. This generalizes the existing results valid for pairwise interactions to the case of complex systems with the most general possible architecture.

Lag synchronization of coupled time-delayed FitzHugh-Nagumo neural networks via feedback control

Synchronization plays a significant role in information transfer and decision-making by neurons and brain neural networks. The development of control strategies for synchronizing a network of chaotic neurons with time delays, different direction-dependent coupling (unidirectional and bidirectional), and noise, particularly under external disturbances, is an essential and very challenging task. Researchers have extensively studied the synchronization mechanism of two coupled time-delayed neurons with bidirectional coupling and without incorporating the effect of noise, but not for time-delayed neural networks. To overcome these limitations, this study investigates the synchronization problem in a network of coupled FitzHugh-Nagumo (FHN) neurons by incorporating time delays, different direction-dependent coupling (unidirectional and bidirectional), noise, and ionic and external disturbances in the mathematical models. More specifically, this study investigates the synchronization of time-delayed unidirectional and bidirectional ring-structured FHN neuronal systems with and without external noise. Different gap junctions and delay parameters are used to incorporate time-delay dynamics in both neuronal networks. We also investigate the influence of the time delays between connected neurons on synchronization conditions. Further, to ensure the synchronization of the time-delayed FHN neuronal networks, different adaptive control laws are proposed for both unidirectional and bidirectional neuronal networks. In addition, necessary and sufficient conditions to achieve synchronization are provided by employing the Lyapunov stability theory. The results of numerical simulations conducted for different-sized multiple networks of time-delayed FHN neurons verify the effectiveness of the proposed adaptive control schemes.

Synchronization Stability Model of Complex Brain Networks: An EEG Study

In this paper, from the perspective of complex network dynamics we investigated the formation of the synchronization state of the brain networks. Based on the Lyapunov stability theory of complex networks, a synchronous steady-state model suitable for application to complex dynamic brain networks was proposed. The synchronization stability problem of brain network state equation was transformed into a convex optimization problem with Block Coordinate Descent (BCD) method. By using Random Apollo Network (RAN) method as a node selection rule, the brain network constructs its subnet work dynamically. We also analyzes the change of the synchronous stable state of the subnet work constructed by this method with the increase of the size of the network. Simulation EEG data from alcohol addicts patients and Real experiment EEG data from schizophrenia patients were used to verify the robustness and validity of the proposed model. Differences in the synchronization characteristics of the brain networks between normal and alcoholic patients were analyzed, so as differences between normal and schizophrenia patients. The experimental results indicated that the establishment of a synchronous steady state model in this paper could be used to verify the synchronization of complex dynamic brain networks and potentially be of great value in the further study of the pathogenic mechanisms of mental illness.