Chimera states emerging from dynamical trapping in chaotic saddles

TL;DR

This paper demonstrates that networks of nonlinear systems with chaotic saddles can form transient chimera states, where some units synchronize periodically while others exhibit chaotic oscillations, with their lifetime depending on coupling parameters.

Contribution

It reveals the emergence of transient chimera states from chaotic saddles in nonlocally coupled networks and analyzes their stability and lifetime dependence on network parameters.

Findings

Identification of two types of transient chimera states with different termination behaviors

Longest chimera lifetime achieved at an optimal coupling range

Synchronized state shown to be asymptotically stable through stability analysis

Abstract

Nonlinear systems possessing nonattracting chaotic sets, such as chaotic saddles, embedded in their state space may oscillate chaotically for a transient time before eventually transitioning into some stable attractor. We show that these systems, when networked with nonlocal coupling in a ring, are capable of forming chimera states, in which one subset of the units oscillates periodically in a synchronized state forming the coherent domain, while the complementary subset oscillates chaotically in the neighborhood of the chaotic saddle constituting the incoherent domain. We find two distinct transient chimera states distinguished by their abrupt or gradual termination. We analyze the lifetime of both chimera states, unraveling their dependence on coupling range and size. We find an optimal value for the coupling range yielding the longest lifetime for the chimera states. Moreover, we implement transversal stability analysis to demonstrate that the synchronized state is asymptotically stable for network configurations studied here.