Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators

We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and as...

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Published in:Journal of physic, complexity complexity, 2024-03, Vol.5 (1), p.15019
Main Authors: Smirnov, L A, Bolotov, M I, Pikovsky, A
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asymmetric coupling
Lyapunov exponent
nonlocal coupling
phase oscillators
traveling chimera
twisted states
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description We explore the model of a population of nonlocally coupled identical phase oscillators on a ring (Abrams and Strogatz 2004 Phys. Rev. Lett. 93 174102) and describe traveling patterns. In the continuous in space formulation, we find families of traveling wave solutions for left-right symmetric and asymmetric couplings. Only the simplest of these waves are stable, which is confirmed by numerical simulations for a finite population. We demonstrate that for asymmetric coupling, a weakly turbulent traveling chimera regime is established, both from an initial standing chimera or an unstable traveling wave profile. The weakly turbulent chimera is a macroscopically chaotic state, with a well-defined synchronous domain and partial coherence in the disordered domain. We characterize it through the correlation function and the Lyapunov spectrum.
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subjects asymmetric coupling
Lyapunov exponent
nonlocal coupling
phase oscillators
traveling chimera
twisted states
title Nonuniformly twisted states and traveling chimeras in a system of nonlocally coupled identical phase oscillators
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