Zou Wei, Sebek Michael, Kiss István Z, Kurths Jürgen
Department of Physics, Hong Kong Baptist University, Kowloon Tong, Hong Kong, China.
Department of Chemistry, Saint Louis University, 3501 Laclede Ave., St. Louis, Missouri 63103, USA.
Chaos. 2017 Jun;27(6):061101. doi: 10.1063/1.4984927.
Amplitude death (AD) and oscillation death (OD) are two structurally different oscillation quenching phenomena in coupled nonlinear systems. As a reverse issue of AD and OD, revival of oscillations from deaths attracts an increasing attention recently. In this paper, we clearly disclose that a time delay in the self-feedback component of the coupling destabilizes not only AD but also OD, and even the AD to OD transition in paradigmatic models of coupled Stuart-Landau oscillators under diverse death configurations. Using a rigorous analysis, the effectiveness of this self-feedback delay in revoking AD is theoretically proved to be valid in an arbitrary network of coupled Stuart-Landau oscillators with generally distributed propagation delays. Moreover, the role of self-feedback delay in reviving oscillations from AD is experimentally verified in two delay-coupled electrochemical reactions.
振幅死亡（AD）和振荡死亡（OD）是耦合非线性系统中两种结构不同的振荡猝灭现象。作为AD和OD的一个逆向问题，振荡从死亡状态的复苏近来受到越来越多的关注。在本文中，我们清楚地揭示了耦合的自反馈分量中的时间延迟不仅会使AD失稳，也会使OD失稳，甚至在不同死亡配置下耦合斯图尔特 - 朗道振子的典型模型中使AD向OD转变。通过严格分析，理论上证明了这种自反馈延迟在撤销AD方面的有效性在具有一般分布传播延迟的任意耦合斯图尔特 - 朗道振子网络中都是有效的。此外，在两个延迟耦合的电化学反应中通过实验验证了自反馈延迟在使振荡从AD状态复苏方面的作用。
