Emergence of multicluster chimera states

Nan Yao; Zi-Gang Huang; Celso Grebogi; Ying-Cheng Lai

doi:10.1038/srep12988

Emergence of multicluster chimera states

Nan Yao, Zi-Gang Huang, Celso Grebogi, Ying-Cheng Lai

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Abstract

A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the struc- turally and dynamically identical oscillators in a coupled networked system spontaneously break into two groups, one exhibiting coherent motion and another incoherent. This phenomenon was typically studied in the setting of non-local coupling configurations. We ask what can happen to chimera states under systematic changes to the network structure when links are removed from the network in an orderly fashion but the local coupling topology remains invariant with respect to an index shift. We find the emergence of multicluster chimera states. Remarkably, as a parameter characterizing the amount of link removal is increased, chimera states of distinct numbers of clusters emerge and per- sist in different parameter regions. We develop a phenomenological theory, based on enhanced or reduced interactions among oscillators in different spatial groups, to explain why chimera states of certain numbers of clusters occur in certain parameter regions. The theoretical prediction agrees well with numerics.

Original language	English
Article number	12988
Journal	Scientific Reports
Volume	5
DOIs	https://doi.org/10.1038/srep12988
Publication status	Published - 9 Sep 2015

Keywords

complex networks
computational science
nonlinear phenomena

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Emergence of multicluster chimera states
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Celso Grebogi
- Mathematical Sciences (Research Theme)
- School of Natural & Computing Sciences, Physics - Sixth Century Chair in Nonlinear & Complex Systems
- Institute for Complex Systems and Mathematical Biology (ICSMB)
Person: Academic

Cite this

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title = "Emergence of multicluster chimera states",

abstract = "A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the struc- turally and dynamically identical oscillators in a coupled networked system spontaneously break into two groups, one exhibiting coherent motion and another incoherent. This phenomenon was typically studied in the setting of non-local coupling configurations. We ask what can happen to chimera states under systematic changes to the network structure when links are removed from the network in an orderly fashion but the local coupling topology remains invariant with respect to an index shift. We find the emergence of multicluster chimera states. Remarkably, as a parameter characterizing the amount of link removal is increased, chimera states of distinct numbers of clusters emerge and per- sist in different parameter regions. We develop a phenomenological theory, based on enhanced or reduced interactions among oscillators in different spatial groups, to explain why chimera states of certain numbers of clusters occur in certain parameter regions. The theoretical prediction agrees well with numerics.",

keywords = "complex networks, computational science, nonlinear phenomena",

author = "Nan Yao and Zi-Gang Huang and Celso Grebogi and Ying-Cheng Lai",

note = "We thank Prof. L. Huang for helpful discussions. This work was partially supported by ARO under Grant No. W911NF-14-1-0504 and by NSF of China under Grant No. 11275003. The visit of NY to Arizona State University was partially sponsored by Prof. Z. Zheng and the State Scholarship Fund of China.",

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AU - Yao, Nan

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AU - Grebogi, Celso

AU - Lai, Ying-Cheng

N1 - We thank Prof. L. Huang for helpful discussions. This work was partially supported by ARO under Grant No. W911NF-14-1-0504 and by NSF of China under Grant No. 11275003. The visit of NY to Arizona State University was partially sponsored by Prof. Z. Zheng and the State Scholarship Fund of China.

PY - 2015/9/9

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N2 - A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the struc- turally and dynamically identical oscillators in a coupled networked system spontaneously break into two groups, one exhibiting coherent motion and another incoherent. This phenomenon was typically studied in the setting of non-local coupling configurations. We ask what can happen to chimera states under systematic changes to the network structure when links are removed from the network in an orderly fashion but the local coupling topology remains invariant with respect to an index shift. We find the emergence of multicluster chimera states. Remarkably, as a parameter characterizing the amount of link removal is increased, chimera states of distinct numbers of clusters emerge and per- sist in different parameter regions. We develop a phenomenological theory, based on enhanced or reduced interactions among oscillators in different spatial groups, to explain why chimera states of certain numbers of clusters occur in certain parameter regions. The theoretical prediction agrees well with numerics.

AB - A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the struc- turally and dynamically identical oscillators in a coupled networked system spontaneously break into two groups, one exhibiting coherent motion and another incoherent. This phenomenon was typically studied in the setting of non-local coupling configurations. We ask what can happen to chimera states under systematic changes to the network structure when links are removed from the network in an orderly fashion but the local coupling topology remains invariant with respect to an index shift. We find the emergence of multicluster chimera states. Remarkably, as a parameter characterizing the amount of link removal is increased, chimera states of distinct numbers of clusters emerge and per- sist in different parameter regions. We develop a phenomenological theory, based on enhanced or reduced interactions among oscillators in different spatial groups, to explain why chimera states of certain numbers of clusters occur in certain parameter regions. The theoretical prediction agrees well with numerics.

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