Abstract
Chimera states are spatiotemporal segregations – stably coexisting coherent and incoherent groups – that can occur in systems of identical phase oscillators. Here we demonstrate that this remarkable phenomenon can also be understood in terms of Pecora and Carroll’s drive-response theory. By calculating the conditional Lyapunov exponents, we show that the incoherent group acts to synchronize the coherent group; the latter playing the role of a response. We also compare the distributions of finite-time conditional Lyapunov exponents to the characteristic distribution that was reported previously for chimera states. The present analysis provides a unifying explanation of the inherently frustrated dynamics that gives rise to chimera states.
Highlights
Chimera states are spatiotemporal segregations – stably coexisting coherent and incoherent groups – that can occur in systems of identical phase oscillators
We show that the present interpretation is consistent with that given previously for the peaks of the characteristic distribution of finite-time Lyapunov exponents for chimera states[16]
Pecora and Carroll’s conditional Lyapunov exponents depend only on the dynamics of the drive, and the prediction they make about the chaos synchronization between the two ‘identical’ systems, are predictions about the behavior of one and the same system; namely, the unaltered ‘drive’ system
Summary
Chimera states are spatiotemporal segregations – stably coexisting coherent and incoherent groups – that can occur in systems of identical phase oscillators. We show that the division of the coupled system of identical oscillators, into the incoherent and coherent groups, corresponds to Pecora and Carroll’s drive-response system.
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