Robustness of chimera states in nonlocally coupled networks of nonidentical logistic maps

Abstract

We investigate the dynamics of nonlocally coupled time-discrete maps with emphasis on the occurrence and robustness of chimera states. These peculiar, hybrid states are characterized by a coexistence of coherent and incoherent regions. We consider logistic maps coupled on a one-dimensional ring with finite coupling radius. Domains of chimera existence form different tongues in the parameter space of coupling range and coupling strength. For a sufficiently large coupling strength, each tongue refers to a wave number describing the structure of the spatial profile. We also analyze the period-adding scheme within these tongues and multiplicity of period solutions. Furthermore, we study the robustness of chimeras with respect to parameter inhomogeneities and find that these states persist for different widths of the parameter distribution. Finally, we explore the spatial structure of the chimera using a spatial correlation function.

Self-adaptation of chimera states

“…Another work on networks of FitzHugh-Nagumo oscillators demonstrated that the chimera states are robust against irregular structural perturbations [63]. Quite recently, the robustness of chimera states in nonlocally coupled networks of nonidentical logistic maps was investigated [54]. These studies indicate that chimera states are generally robust against various kinds of external perturbations.…”

Image Entropy for the Identification of Chimera States of Spatiotemporal Divergence in Complex Coupled Maps of Matrices

“…A paradigmatic model of a lattice of translational invariance with periodic boundary conditions, comprising m real-valued, single-variable time-discrete maps that are coupled to their closest neighbors reads [ 14 ]: where i is the number of the node ( ); t is discrete time ( ); is the scalar nodal variable; is the coupling parameter within the interval ; P is a fixed number of nearest neighbors to either side ( ). The local dynamics of every element i on the one-dimensional ring is described by the Logistic map: where and the initial condition is bounded to in order to ensure the mapping to the interval [ 30 ].…”

“…Initially it was thought that chimeras can be observed only in networks of non-locally coupled oscillators [ 1 ]. Later studies revealed that besides non-locally connected networks [ 3 , 4 , 13 , 14 , 15 , 16 ], these states can be found in local [ 17 , 18 , 19 ] as well as in global [ 6 , 20 ] coupling topologies. Chimera patterns are analyzed in networks of Logistic maps with hierarchical connectivities [ 21 ].…”

Relay and complete synchronization in heterogeneous multiplex networks of chaotic maps

“…12,13,39 Chimera states were first discovered in ensembles of nonlocally coupled identical Kuramoto oscillators. 12,39 Afterward, they were found in networks of oscillatory systems with periodic and chaotic dynamics, [26][27][28][29][40][41][42][43][44][45][46][47][48][49][50] in neural networks, [51][52][53][54][55] and also for global and local coupling [56][57][58][59][60] between the elements. Chimeras were also observed in a number of experiments.…”