Synchronization transition in networked chaotic oscillators: The viewpoint from partial synchronization

Fu, Chenbo; Lin, Weijie; Huang, Liang; Wang, Xingang

doi:10.1103/physreve.89.052908

Cited by 36 publications

(33 citation statements)

References 55 publications

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“…Yet recent studies give the accumulating evidences which show that cluster synchronization is also observable in complex networks [17,18,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The first batch of evidences come from the synchronization of small-size complex network possessing reflection symmetries [14,17,19,40,42], where it is found, in spite of the presence of random shortcut links, the oscillators can be synchronized in pairs according to the network reflection symmetries. Additional evidences from large-size complex network possessing permutation symmetries have been also provided [43][44][45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Chen

Wang

et al. 2018

Front. Phys.

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By a small-size complex network of coupled chaotic Hindmarsh-Rose circuits, we study experimentally the stability of network synchronization to the removal of shortcut links. It is shown that the removal of a single shortcut link may destroy either completely or partially the network synchronization. Interestingly, when the network is partially desynchronized, it is found that the oscillators can be organized into different groups, with oscillators within each group being highly synchronized but are not for oscillators from different groups, showing the intriguing phenomenon of cluster synchronization. The experimental results are analyzed by the method of eigenvalue analysis, which implies that the formation of cluster synchronization is crucially dependent on the network symmetries. Our study demonstrates the observability of cluster synchronization in realistic systems, and indicates the feasibility of controlling network synchronization by adjusting network topology. *

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Section: Introductionmentioning

confidence: 99%

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Chen

Wang

et al. 2018

Front. Phys.

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“…To give deeper insights into the synchronous transition, particularly from CSO to PS as a function of ρ, we below using master stability function (MSF) [43][44][45] approach to quantitatively characterize the synchronous boundary separating these two regimes. As discussed previously, Eqs.…”

Section: B Master Stability Function Approachmentioning

confidence: 99%

Quorum Sensing in Populations of Spatially Extended Chaotic Oscillators Coupled Indirectly via a Heterogeneous Environment

Cao

2017

J Nonlinear Sci

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Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless, most of previous works considered the homogeneous case only. Here, we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states such as oscillation death, phase synchronization, and complete synchronized oscillation as well as their transitions were found. More importantly, we uncovered a non-traditional quorum sensing transition: increasing the density would first lead to collective oscillation from oscillation quench, but further increasing the population density would lead to degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. Further more, by treating the indirectly coupled systems effectively to the system with directly local coupling, we applied the master stability function approach to predict the occurrence of the complete synchronized oscillation, which were in agreement with the direct numerical simulations of the full system. The possible candidates of the experimental realization on our model was also discussed.

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“…Very recently, some of the authors and co-workers studied the desynchronous pattern of networked dynamics in detail [49,50]. We took a closer look at the nonzero time-averaged synchronization errors for each node and found that they are linearly related to the absolute value of the eigenvector element of the Laplacian matrix with the corresponding critical mode of the coupled systems.…”

Section: Introductionmentioning

confidence: 98%

Control for a synchronization-desynchronization switch

et al. 2014

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How to freely enhance or suppress synchronization of networked dynamical systems is of great importance in many disciplines. A unified precise control method for a synchronization-desynchronization switch, called the pull-push control method, is suggested. Namely, synchronization can be achieved when the original systems are desynchronous by pulling (or protecting) one node or a certain subset of nodes, whereas desynchronization can be accomplished when the systems are already synchronous by pushing (or kicking) one node or a certain subset of nodes. With this method, the controlled nodes should be chosen by the generalized eigenvector centrality of the critical synchronization mode of the Laplacian matrix. Compared with existing control methods for synchronization, it displays high efficiency, flexibility, and precision as well.

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Synchronization transition in networked chaotic oscillators: The viewpoint from partial synchronization

Cited by 36 publications

References 55 publications

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

Quorum Sensing in Populations of Spatially Extended Chaotic Oscillators Coupled Indirectly via a Heterogeneous Environment

Control for a synchronization-desynchronization switch

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