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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 exponential coupling kernel.(a) 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. (b) Regions of m-cluster chimera states predicted by the mutual-enhancement theory (the colored thick horizontal lines at different m levels), including the main regions m = 3 and 2, and the subregion 2&4 for the 2&4-cluster chimera states. The gray and white backgrounds denote the regions of the m-cluster chimera states obtained from Eq. (1) and Eq. (5), respectively. The subregion for the 2&4-cluster chimera states obtained from Eqs (1) and (5) is within η = 0.76 and 0.91 as marked by the two thin black vertical lines. The exponential coupling kernel has κ = 4, and the phase lag is α = 1.457.
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f5: Enhancement factor and predicted regions of multicluster chimera states for exponential coupling kernel.(a) 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. (b) Regions of m-cluster chimera states predicted by the mutual-enhancement theory (the colored thick horizontal lines at different m levels), including the main regions m = 3 and 2, and the subregion 2&4 for the 2&4-cluster chimera states. The gray and white backgrounds denote the regions of the m-cluster chimera states obtained from Eq. (1) and Eq. (5), respectively. The subregion for the 2&4-cluster chimera states obtained from Eqs (1) and (5) is within η = 0.76 and 0.91 as marked by the two thin black vertical lines. The exponential coupling kernel has κ = 4, and the phase lag is α = 1.457.

Mentions: where xi and xj run from 0 to 1 with periodic boundary condition7. Figure 5(a) presents the curves of I(η) from Eq. (8) with integral interval [η, 1], while Fig. 5(b) compares the prediction (the colored thick horizontal lines) with results from simulations of Eq. (1) (the gray and white regions). We observe a good agreement. The corresponding spatiotemporal patterns for a representative set of η values (0.51, 0.67, 0.72, and 0.79) are shown in Fig. 6.


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 exponential coupling kernel.(a) 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. (b) Regions of m-cluster chimera states predicted by the mutual-enhancement theory (the colored thick horizontal lines at different m levels), including the main regions m = 3 and 2, and the subregion 2&4 for the 2&4-cluster chimera states. The gray and white backgrounds denote the regions of the m-cluster chimera states obtained from Eq. (1) and Eq. (5), respectively. The subregion for the 2&4-cluster chimera states obtained from Eqs (1) and (5) is within η = 0.76 and 0.91 as marked by the two thin black vertical lines. The exponential coupling kernel has κ = 4, and the phase lag is α = 1.457.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f5: Enhancement factor and predicted regions of multicluster chimera states for exponential coupling kernel.(a) 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. (b) Regions of m-cluster chimera states predicted by the mutual-enhancement theory (the colored thick horizontal lines at different m levels), including the main regions m = 3 and 2, and the subregion 2&4 for the 2&4-cluster chimera states. The gray and white backgrounds denote the regions of the m-cluster chimera states obtained from Eq. (1) and Eq. (5), respectively. The subregion for the 2&4-cluster chimera states obtained from Eqs (1) and (5) is within η = 0.76 and 0.91 as marked by the two thin black vertical lines. The exponential coupling kernel has κ = 4, and the phase lag is α = 1.457.
Mentions: where xi and xj run from 0 to 1 with periodic boundary condition7. Figure 5(a) presents the curves of I(η) from Eq. (8) with integral interval [η, 1], while Fig. 5(b) compares the prediction (the colored thick horizontal lines) with results from simulations of Eq. (1) (the gray and white regions). We observe a good agreement. The corresponding spatiotemporal patterns for a representative set of η values (0.51, 0.67, 0.72, and 0.79) are shown in Fig. 6.

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