Cluster Synchronization Research Articles

Competition during verbal creative processes influences on ERS/ERD

ABSTRACT Humans are social creatures, and many tasks in our daily lives are solved together. The two main forms of social interaction in problem solving could be defined as competition and cooperation. In our study, we compared the ERS/ERD when performing a creative task (Alternative Uses Test, AUT) and a control task (“naming the objects from the presented category”) under competitive conditions in dyads (22 dyads, m-m, f-f, 18–23 years old) compared to the performance of tasks individually. The number of answers given by subjects under competitive conditions was significantly lower than during the execution of the tasks individually. The solving of the creative task in competition versus individual performance was accompanied by EEG synchronization (9–30 hz) clusters: 140–1220 ms and 900–1780 ms after stimulus presentation; 13.5–30 hz (1800–1980 ms), reflecting the creative thinking mode, and expected cognitive, emotional answers’ assessment. The control task under competitive conditions was accompanied by pronounced synchronization of low frequencies in the frontal areas (2–7 hz, 0–1980 ms), due to a greater working memory load; synchronization clusters in broadband (10–30 hz, 100–320 ms, 400–860 ms) and in the beta EEG band (17–30 hz, 1140–1980 ms). The competitive conditions significantly modulated the brain activity underlying creative and non-creative cognitive task performance, and resulted in greater induced EEG synchronization.

Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel

In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.

Two-cluster synchronization in a fully coupled network of Mackey–Glass generators

We study a fully connected network of Mackey–Glass generators, each described by the Mackey–Glass delay differential equation. This system can exhibit non-trivial behaviour over time. One interesting scenario of such behaviour is cluster synchronization—regimes in which all components are divided into several groups, each oscillating in the same mode. Cluster synchronization can appear in various systems, such as neural networks and biological systems. In this work, we investigate the case of two-cluster synchronization and prove the existence of such modes.

Neuron configuration enhances the synchronization dynamics in ring networks with heterogeneous firing patterns

Neuron synchronization is fundamental for brain dynamics. While several efforts have been made to understand neuron coupling between tonic and bursting neurons, the position of neurons in a neural network and its relationship with synchronization is not fully understood. This work investigates the impact of neuronal heterogeneity on firing pattern transitions and synchronization in networks comprising tonic and bursting neurons. Using the Huber-Braun model, we explore two configurations: one with neurons grouped closely and another with maximal separation. Our findings reveal that while increased coupling strength generally promotes synchronization, the specific mix of neuron types and their spatial configuration crucially modulate both synchronization and firing pattern transitions, leading to phenomena such as cluster synchronization and global phase synchrony. The results indicate that the configuration with maximal separation and with mostly bursting neurons synchronizes more quickly. Firing pattern transitions are also configuration-dependent. For example, in the network with half tonic and half bursting, the configuration grouped closely undergoes diverse complex dynamics transition in the synchronized state, while the other configuration synchronize with chaotic bursting dynamics. Behaviors like cluster synchronization are observed in this network. The study underscores the significance of considering neuronal heterogeneity in understanding network dynamics.

Resonance-induced synchronization in coupled phase oscillators with bimodal frequency distribution and periodic coupling.

Synchronization behaviors in globally coupled phase oscillators with symmetric bimodal frequency distribution and periodic coupling are studied. It is found that by a proper setting of the frequency of the periodic coupling, the synchronization propensity of the oscillators can be markedly improved. Specifically, we show that when the frequency of the periodic coupling matches the distance of the central frequencies in the distribution, the critical coupling characterizing the onset of synchronization can be substantially decreased. The mechanism behind the phenomenon of periodic-coupling-enhanced synchronization is analyzed by the methods of Ott-Antonsen ansatz and synchronization transition tree, and it is revealed that the synchronization enhancement is attributed to the resonance between the synchronization clusters and the periodic coupling.

Existence and Stability Criteria for Global Synchrony and for Synchrony in two Alternating Clusters of Pulse-Coupled Oscillators Updated to Include Conduction Delays.

37N25, 39A06, 39A30, 92B25, 92C20.

Cluster synchronization of fractional-order coupled genetic regulatory networks via pinning control

Cell-to-cell interaction and quorum sensing are universal in real life and have an extremely important biological significance. Besides, fractional-order calculus has tremendous advantages in describing the memory of neurons and the inheritance of genes. In this article, the cluster synchronization of fractional-order coupled genetic regulatory networks (GRNs) is explored by applying pinning control technique. First of all, a type of coupled fractional-order models about GRNs is proposed based on the quorum sensing and cluster expression characteristics of genes. Secondly, by designing pinning control strategies and fractional-order inequalities, several sufficient criteria are constructed to reach cluster synchronization. Furthermore, the selection rule of pining nodes is provided to conduct what nodes can be selected to be pinned and how many nodes are pinned to achieve cluster synchronization. In addition, the fractional-order adaptive control strategy is designed to regulate control gains. Several numerical results are provided lastly to confirm the theoretical analysis.

Finite-time cluster synchronization of multi-weighted fractional-order coupled neural networks with and without impulsive effects

In this paper, finite-time cluster synchronization (FTCS) of multi-weighted fractional-order neural networks is studied. Firstly, a FTCS criterion of the considered neural networks is obtained by designing a new delayed state feedback controller. Secondly, a FTCS criterion for the considered neural networks with mixed impulsive effects is given by constructing a new piecewise controller, where both synchronizing and desynchronizing impulses are taken into account. It should be noted that it is the first time that finite-time cluster synchronization of multi-weighted neural networks has been investigated. Finally, numerical simulations are given to show the validity of the theoretical results.

Finite/fixed-time cluster synchronization for directed and multiplex coupled dynamic networks

This article deals with finite/fixed-time cluster synchronization (FnTCS/FdTCS) issue for directed and multiplex coupled dynamic networks (MCDNs). Finite/fixed-time synchronization of multiplex networks has become a popular research topic, which indicates that, state information is utilized for synchronization, and the settling time depends on original condition for a range of finite time, while the time is bounded with arbitrary original value for fixed-time one. Through constructing appropriate feedback control protocol, FnTCS and FdTCS matters for MCDNs are settled under re-arranging variables' order technique. The present model contains the case that outer matrices (OMs) can be directed, with competitive elements, and not even connected, while previous and related researches assumed that OMs were undirected, cooperative and connected, so existing results can be improved for more general and broader regulations. This strategy above is presented to solve directed CDNs with multiweights from angle of inner and outer matrices, and we prove that if the weighted group of added OMs for each dimension is strongly connected, then cluster synchronization rules are established in finite/fixed time. Moreover, we also earn finite/fixed-time synchronization criteria when the cluster is single. In addition, the issue of FnTCS/FdTCS is developed for directed and multiplex coupled reaction-diffusion networks (MCRDNs) as an application. The validity of these gained results is verified by simulated examples.

Scalable synchronization cluster in networked chaotic oscillators.

Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the other oscillators remain desynchronized. Interestingly, with the increase in the coupling strength, the cluster is expanding gradually by recruiting the desynchronized oscillators one by one. This new synchronization phenomenon, which is named "scalable synchronization cluster," is explored theoretically by the method of eigenvector-based analysis, and it is revealed that the scalability of the cluster is attributed to the unique feature of the eigenvectors of the network coupling matrix. The transient dynamics of the cluster in response to random perturbations are also studied, and it is shown that in restoring to the synchronization state, oscillators inside the cluster are stabilized in sequence, illustrating again the hierarchy of the oscillators. The findings shed new light on the collective behaviors of networked chaotic oscillators and are helpful for the design of real-world networks where scalable synchronization clusters are concerned.

Secure impulsive cluster synchronization control of complex dynamical networks with parameter mismatches under deception attacks

The issue of secure cluster synchronization (SCS) of complex dynamical networks (CDNs) with parameter mismatches under deception attacks is investigated in this article. Firstly, the deception attacks are supposed to inject false information into controller-to-actuator channels, while the occurrences of deception attack are always subject to Bernoulli distribution. Secondly, an improved pinning impulsive control strategy is designed. The impulsive gain in the control strategy is take from a new range. Moreover, we obtain the estimation of synchronization error upper bound and boundaries of secure synchronization region. The synchronization error will converge to a bounded ball that depends on attack energy at a exponential rate. The CDNs without deception attacks under pinning impulsive control can achieve complete cluster synchronization. Finally, two numerical examples with 20 nodes based on MATLAB software are presented to demonstrate the effectiveness of the theoretical results.

How do the eigenvalues of the Laplacian matrix affect route to synchronization patterns?

In cluster synchronization, network nodes are divided into synchronized groups before the whole network gets synchronized. This phenomenon is crucial in understanding the mechanism behind the synchronization of real-world and man-made complex networks like neuronal networks and power grids. The Laplacian matrix and its eigenvalues provide helpful information about the networks' synchronization, robustness, and controllability. Here, analyzing the relation between the Laplacian matrix eigenvalues and cluster synchronization demonstrates that the intensity of the eigenvalues has significant importance on the clusters' appearance. Results show that considering groups of equal eigenvalues yields the appearing of clusters in the network. So, this technique allows the ability to design networks with the desired number of clusters with defined cluster size. Synchronization of the clusters results in a plateau in the order parameter evolution. Furthermore, studying two different chaotic systems shows that this relationship depends on the systems' dynamics. Here, the eigenvector centrality tool is utilized to examine the existence of clusters besides the graph representation.

Cluster synchronization control for the complex network with dynamic connection relations

AbstractIn this article, the cluster synchronization control for a complex dynamic network (CDN) with mutually coupled nodes subsystem (NS) and connection relations subsystem is investigated. The process of cluster synchronization is segmented into three dynamic continuous stages: first, the free movement, then the task‐oriented clustering, and finally the cluster synchronization. The control scheme, founded on the clustering nodes of CDN, is proposed, such that the cluster synchronization arises when clustering all the nodes into two different sub‐networks (SNs). This approach originates from the flight motion for a group of autonomous aircrafts. At a certain moment, free flight is interrupted, and all the aircrafts split into two SNs according to the given clustering rules. Then the two controlled SNs are required to achieve cluster synchronization, that is, every SN converges to the same in speed. In order to split all the nodes into two different SNs, a clustering algorithm according to the “central nodes” is proposed. Based on Lyapunov stability theory, by designing the suitable inner cluster links, the adaptive controller of NS for each SN is synthesized to guarantee the stability of the error system. It is shown that the eventual inner topology of each SN is displayed in the pre‐given form when the cluster synchronization achieves. Finally, the merits and effectiveness of the proposed control scheme are verified by a simulation example.

Prescribed-time cluster synchronization of coupled inertial neural networks: a lifting dimension approach

Prescribed-time cluster synchronization of coupled inertial neural networks: a lifting dimension approach

Cluster formation due to repulsive spanning trees in attractively coupled networks.

Ensembles of coupled nonlinear oscillators are a popular paradigm and an ideal benchmark for analyzing complex collective behaviors. The onset of cluster synchronization is found to be at the core of various technological and biological processes. The current literature has investigated cluster synchronization by focusing mostly on the case of attractive coupling among the oscillators. However, the case of two coexisting competing interactions is of practical interest due to their relevance in diverse natural settings, including neuronal networks consisting of excitatory and inhibitory neurons, the coevolving social model with voters of opposite opinions, and ecological plant communities with both facilitation and competition, to name a few. In the present article, we investigate the impact of repulsive spanning trees on cluster formation within a connected network of attractively coupled limit-cycle oscillators. We successfully predict which nodes belong to each cluster and the emergent frustration of the connected networks independent of the particular local dynamics at the network nodes. We also determine local asymptotic stability of the cluster states using an approach based on the formulation of a master stability function. We additionally validate the emergence of solitary states and antisynchronization for some specific choices of spanning trees and networks.

Fibration symmetries and cluster synchronization in the Caenorhabditis elegans connectome.

Capturing how the Caenorhabditis elegans connectome structure gives rise to its neuron functionality remains unclear. It is through fiber symmetries found in its neuronal connectivity that synchronization of a group of neurons can be determined. To understand these we investigate graph symmetries and search for such in the symmetrized versions of the forward and backward locomotive sub-networks of the Caenorhabditi elegans worm neuron network. The use of ordinarily differential equations simulations admissible to these graphs are used to validate the predictions of these fiber symmetries and are compared to the more restrictive orbit symmetries. Additionally fibration symmetries are used to decompose these graphs into their fundamental building blocks which reveal units formed by nested loops or multilayered fibers. It is found that fiber symmetries of the connectome can accurately predict neuronal synchronization even under not idealized connectivity as long as the dynamics are within stable regimes of simulations.

Asymmetric leader-laggard cluster synchronization for collective decision-making with laser network

Photonic accelerators have recently attracted soaring interest, harnessing the ultimate nature of light for information processing. Collective decision-making with a laser network, employing the chaotic and synchronous dynamics of optically interconnected lasers to address the competitive multi-armed bandit (CMAB) problem, is a highly compelling approach due to its scalability and experimental feasibility. We investigated essential network structures for collective decision-making through quantitative stability analysis. Moreover, we demonstrated the asymmetric preferences of players in the CMAB problem, extending its functionality to more practical applications. Our study highlights the capability and significance of machine learning built upon chaotic lasers and photonic devices.

Controlling spatiotemporal dynamics of neural networks by Lévy noise.

We explore numerically how additive Lévy noise influences the spatiotemporal dynamics of a neural network of nonlocally coupled FitzHugh-Nagumo oscillators. Without noise, the network can exhibit various partial or cluster synchronization patterns, such as chimera and solitary states, which can also coexist in the network for certain values of the control parameters. Our studies show that these structures demonstrate different responses to additive Lévy noise and, thus, the dynamics of the neural network can be effectively controlled by varying the scale parameter and the stability index of Lévy noise. Specifically, introducing Lévy noise in the multistability mode can increase the probability of observing chimera states while suppressing solitary states. Nonetheless, decreasing the stability parameter enables one to diminish the noise effect on chimera states and amplify it on solitary states.

Cluster synchronization of fractional‐order complex networks via variable‐time impulsive control

This paper investigates the cluster synchronization of fractional‐order complex networks. Considering that impulsive control can reduce the update of controller, and the appearance of impulse is always dependent on each node in the networks instead of appearing at fixed instant, thus we design a variable‐time impulsive controller to control the considered networks. Foremost, several assumptions are proposed to guarantee the every solution of coupled error networks intersect each discontinuous impulsive surface exactly once. In addition, by utilizing the B‐equivalence method and the theory of fractional calculus, the variable‐time impulsive fractional‐order system is reduced to a fixed‐time impulsive fractional‐order system, which can be regarded as the comparison system of the former. Next, under the framework of 1‐norm, some sufficient conditions are presented to ensure that fractional‐order system and target trajectory ultimately achieve cluster synchronization. In the end, a numerical example is designed to illustrate the validity and feasibility of theoretical results.

Rotating clusters in phase-lagged Kuramoto oscillators with higher-order interactions.

The effect of phase-lag in pairwise interactions has been a topic of great interest for a while. However, real-world systems often have interactions that are beyond pairwise and can be modeled using simplicial complexes. We show that the inclusion of higher-order interactions in phase-lagged coupled Kuramoto oscillators shifts the critical point at which first-order transition from a cluster synchronized state to an incoherent state takes place. Considering the polar coordinates, we obtain the rotation frequency of the clusters, which turns out to be a function of the phase-lag parameter. In turn, the phase- lag can be used as a control parameter to achieve a desired cluster frequency. Moreover, in the thermodynamic limit, by employing the Ott-Antonsen approach we derive a reduced equation for the order parameter measuring cluster synchronization and progress further through the self-consistency method to obtain a closed form of the order parameter measuring global synchronization which was lacking in the Ott-Antonsen approach.