Limits...
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

Nodal connection structure after link removal.For any node in the network, removal of links starts from the nodes with the minimum distance to it (colored by red).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4563257&req=5

f1: Nodal connection structure after link removal.For any node in the network, removal of links starts from the nodes with the minimum distance to it (colored by red).

Mentions: where ϕ(xi) is the phase of the ith oscillator at position xi. For convenience, we choose the range of the spatial variable to be [−π,π]. Since the oscillators are identical, the natural velocity and phase lag parameter, ω and α, respectively, are chosen to be constants that do not depend on the spatial location of the oscillator. Without loss of generality, we set ω = 0 and choose α  <  π/2. The kernel G(xi − xj) = [1 + Acos(xi − xj)]/(2π) is a non-negative even function that characterizes the non-local coupling among all the oscillators. The quantity cij is the ij th element of the N × N coupling matrix C, where Cij = 1 if there is coupling from the jth oscillator to the i th oscillator, and Cij = 0 indicates the absence of such coupling. We systematically remove certain fraction of links from every node, while ensuring that all nodes remain identical and structurally indistinguishable. To do this we introduce a tunable topological parameter η = 2L/N (L = 1, . . . , N/2), the fraction of neighbors removed for any given oscillator, where L denotes the number of removed links from each side of the node. We have Cij = 0 for j = i − L, . . . , i + L. The connection pattern of a node after link removal is shown in Fig. 1, where the node was originally connected to all other nodes in the network, and link removal is carried out in the order of increasing distance from this node.


Emergence of multicluster chimera states.

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

Nodal connection structure after link removal.For any node in the network, removal of links starts from the nodes with the minimum distance to it (colored by red).
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f1: Nodal connection structure after link removal.For any node in the network, removal of links starts from the nodes with the minimum distance to it (colored by red).
Mentions: where ϕ(xi) is the phase of the ith oscillator at position xi. For convenience, we choose the range of the spatial variable to be [−π,π]. Since the oscillators are identical, the natural velocity and phase lag parameter, ω and α, respectively, are chosen to be constants that do not depend on the spatial location of the oscillator. Without loss of generality, we set ω = 0 and choose α  <  π/2. The kernel G(xi − xj) = [1 + Acos(xi − xj)]/(2π) is a non-negative even function that characterizes the non-local coupling among all the oscillators. The quantity cij is the ij th element of the N × N coupling matrix C, where Cij = 1 if there is coupling from the jth oscillator to the i th oscillator, and Cij = 0 indicates the absence of such coupling. We systematically remove certain fraction of links from every node, while ensuring that all nodes remain identical and structurally indistinguishable. To do this we introduce a tunable topological parameter η = 2L/N (L = 1, . . . , N/2), the fraction of neighbors removed for any given oscillator, where L denotes the number of removed links from each side of the node. We have Cij = 0 for j = i − L, . . . , i + L. The connection pattern of a node after link removal is shown in Fig. 1, where the node was originally connected to all other nodes in the network, and link removal is carried out in the order of increasing distance from this node.

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