Hyperbolicity impedes emergence of chimera states in networks of nonlocally coupled chaotic oscillators

Abstract

We analyze nonlocally coupled networks of identical chaotic oscillators with either time-discrete or time-continuous dynamics (Henon map, Lozi map, Lorenz system). We hypothesize that chimera states, in which spatial domains of coherent (synchronous) and incoherent (desynchronized) dynamics coexist, can be obtained only in networks of nonhyperbolic chaotic systems and cannot be found in networks of hyperbolic systems. This hypothesis is supported by analytical results and numerical simulations for hyperbolic and nonhyperbolic cases.

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• Relay synchronization in multiplex networks of discrete maps
• Mechanism for Strong Chimeras
• Delay-induced chimeras in neural networks with fractal topology
• Critical Switching in Globally Attractive Chimeras
• Chimera states in networks of logistic maps with hierarchical connectivities
• Riddling: Chimera's dilemma
• Identification of Chimera using Machine Learning
• Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators
• Transition from chimera/solitary states to traveling waves
• Synchronization scenarios in three-layer networks with a hub
• Chimeras and clusters in networks of hyperbolic chaotic oscillators
• Engineering chimera patterns in networks using heterogeneous delays
• Transient Chaos Generates Small Chimeras
• Taming Chimeras in Networks through Multiplexing Delays
• Impact of pulse exposure on chimera state in ensemble of FitzHugh-Nagumo systems
• Coupling-induced periodic windows in networked discrete-time systems