Department of Physics, University of South Africa, Science Campus, Private Bag X6, Florida 1710, South Africa.
Sci Rep. 2016 Jul 4;6:29213. doi: 10.1038/srep29213.
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.
我们对嵌合体状态的着迷部分源于相同且完全耦合的振荡器分裂成空间上分离的、相干和非相干振荡群的有点矛盾但基本的特性。虽然已经检测到各种类型嵌合体的系统列表在继续增长，但旨在阐明这种惊人行为的基本原因的数学分析数量也相应增加。基于模型系统，有强烈的迹象表明，嵌合体状态可能普遍存在于包含大量耦合振荡器的自然发生系统中 - 例如某些生物系统和高温超导材料。在这项工作中，我们提出了一种检测和表征嵌合体状态的新方法。具体来说，结果表明，对应于嵌合体状态的有限时间李雅普诺夫指数的概率密度具有确定的特征形状。这种分布可作为嵌合体状态的特征，特别是在无法直接测量所有振荡器相位的系统中。对于这种情况，我们建议可以通过标准嵌入技术重建特征分布来检测嵌合体状态，从而有可能在其他情况下检测到它们存在的系统中检测到嵌合体状态。
