Abstract
Our fascination with chimera states stems partially from the somewhat paradoxical, yet fundamental trait of identical, and identically coupled, oscillators to split into spatially separated, coherently and incoherently oscillating groups. While the list of systems for which various types of chimeras have already been detected continues to grow, there is a corresponding increase in the number of mathematical analyses aimed at elucidating the fundamental reasons for this surprising behaviour. Based on the model systems, there are strong indications that chimera states may generally be ubiquitous in naturally occurring systems containing large numbers of coupled oscillators – certain biological systems and high-Tc superconducting materials, for example. In this work we suggest a new way of detecting and characterising chimera states. Specifically, it is shown that the probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a definite characteristic shape. Such distributions could be used as signatures of chimera states, particularly in systems for which the phases of all the oscillators cannot be measured directly. For such cases, we suggest that chimera states could perhaps be detected by reconstructing the characteristic distribution via standard embedding techniques, thus making it possible to detect chimera states in systems where they could otherwise exist unnoticed.
Highlights
Fascinating experiments, chimera states may be of physical importance in systems of Josephson junctions (JJs)[33,34,35]
The spontaneous appearance of chimera states was found in numerical simulations of so-called superconducting quantum interference devices (SQUIDs) metamaterials[36]
The distribution of local Lyapunov exponents (LLEs) for a stack of intrinsic JJs could be obtained from a sufficiently long time series of the total voltage across the stack; making it possible to detect the existence of a chimera state in the stack
Summary
Fascinating experiments, chimera states may be of physical importance in systems of Josephson junctions (JJs)[33,34,35]. 51 the positions of the peaks in the distributions of LLEs were used to characterise the time evolution of intermittent chaotic chimeras occurring in coupled Kuramoto oscillators with inertia.
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