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Emergence of multicluster chimera states.

Yao N, Huang ZG, Grebogi C, Lai YC - Sci Rep (2015)

Bottom Line: 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.The theoretical prediction agrees well with numerics.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, Xi'an University of Technology, Xi'an 710054, China.

ABSTRACT
A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the structurally 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 persist 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.

No MeSH data available.


Related in: MedlinePlus

Enhancement factor and predicted regions of multicluster chimera states for rectangular coupling kernel.Enhancement factor I as a function of η for different values of m. The regions of maximum I values among the different m curves (specified as bold lines) are the regions in which the corresponding m-cluster chimera states emerge. The results in (a) are for N = 1024 and γ = 0.6, and those in (b) are for N = 512 and γ = 0.8.
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f7: Enhancement factor and predicted regions of multicluster chimera states for rectangular coupling kernel.Enhancement factor I as a function of η for different values of m. The regions of maximum I values among the different m curves (specified as bold lines) are the regions in which the corresponding m-cluster chimera states emerge. The results in (a) are for N = 1024 and γ = 0.6, and those in (b) are for N = 512 and γ = 0.8.

Mentions: where xi and xj run from −1 to 1 with periodic boundary condition, and is a parameter characterizing the width of the coupling range for oscillators. The behaviors of I(η) and a number of typical spatiotemporal patterns are shown in Fig. 7(a,b), for γ = 0.6 and 0.8, respectively. The results are essentially the same as those for the case of sinusoidal coupling function, demonstrating the general applicability of our mutual-enhancement theory.


Emergence of multicluster chimera states.

Yao N, Huang ZG, Grebogi C, Lai YC - Sci Rep (2015)

Enhancement factor and predicted regions of multicluster chimera states for rectangular coupling kernel.Enhancement factor I as a function of η for different values of m. The regions of maximum I values among the different m curves (specified as bold lines) are the regions in which the corresponding m-cluster chimera states emerge. The results in (a) are for N = 1024 and γ = 0.6, and those in (b) are for N = 512 and γ = 0.8.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4563257&req=5

f7: Enhancement factor and predicted regions of multicluster chimera states for rectangular coupling kernel.Enhancement factor I as a function of η for different values of m. The regions of maximum I values among the different m curves (specified as bold lines) are the regions in which the corresponding m-cluster chimera states emerge. The results in (a) are for N = 1024 and γ = 0.6, and those in (b) are for N = 512 and γ = 0.8.
Mentions: where xi and xj run from −1 to 1 with periodic boundary condition, and is a parameter characterizing the width of the coupling range for oscillators. The behaviors of I(η) and a number of typical spatiotemporal patterns are shown in Fig. 7(a,b), for γ = 0.6 and 0.8, respectively. The results are essentially the same as those for the case of sinusoidal coupling function, demonstrating the general applicability of our mutual-enhancement theory.

Bottom Line: 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.The theoretical prediction agrees well with numerics.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, Xi'an University of Technology, Xi'an 710054, China.

ABSTRACT
A remarkable phenomenon in spatiotemporal dynamical systems is chimera state, where the structurally 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 persist 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.

No MeSH data available.


Related in: MedlinePlus