Chaotic macroscopic phases in one-dimensional oscillators
Chaotic macroscopic phases in one-dimensional oscillators
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一维振荡器中的混沌宏观相
DOI：
10.1140/epjst/e2017-70056-4
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
E. Ullner
中科院分区：
文献类型：
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作者：
A. Politi;A. Pikovsky;E. Ullner
在一维振子的平均场模型中，深入分析了集体混沌的宏观描述与微观动力学之间的联系。我们研究了微观构型的无穷小扰动在多大程度上也能提供有关相应宏观相稳定性的信息。在相同的一维动力单元的集合中，有可能表示微观构型，从而使它们与宏观世界的联系透明。结果，我们发现了一个中间的、介观的、距离范围的证据，在这个范围内，不稳定性既不受微观方程的控制，也不受宏观方程的控制。我们研究了一系列的指标，从通常的微观李雅普诺夫指数，到集体指数，包括有限振幅指数。本文还简要回顾了一个脉冲耦合振子系统，作为自发产生集体混沌的非同相振子的一个例子。
The connection between the macroscopic description of collective chaos and the underlying microscopic dynamics is thoroughly analysed in mean-field models of one-dimensional oscillators. We investigate to what extent infinitesimal perturbations of the microscopic configurations can provide information also on the stability of the corresponding macroscopic phase. In ensembles of identical one-dimensional dynamical units, it is possible to represent the microscopic configurations so as to make transparent their connection with the macroscopic world. As a result, we find evidence of an intermediate, mesoscopic, range of distances, over which the instability is neither controlled by the microscopic equations nor by the macroscopic ones. We examine a whole series of indicators, ranging from the usual microscopic Lyapunov exponents, to the collective ones, including finite-amplitude exponents. A system of pulse-coupled oscillators is also briefly reviewed as an example of non-identical phase oscillators where collective chaos spontaneously emerges.