Department of Electrical and Information Systems, Osaka Prefecture University, 1-1 Gakuen-cho, Naka-ku, Sakai, Osaka 599-8531 Japan.
Phys Rev E. 2017 Jun;95(6-1):062220. doi: 10.1103/PhysRevE.95.062220. Epub 2017 Jun 23.
This paper shows that, in a pair of one-dimensional complex Ginzburg-Landau (CGL) systems, diffusive connections can induce amplitude death. Stability analysis of a spatially uniform steady state in coupled CGL systems reveals that amplitude death never occurs in a pair of identical CGL systems coupled by no-delay connection, but can occur in the case of delay connection. Moreover, amplitude death never occurs in coupled identical CGL systems with zero nominal frequency. Based on these analytical results, we propose a procedure for designing the connection delay time and the coupling strength to induce spatial-robust stabilization, that is, a stabilization of the steady state for any system size and any boundary condition. Numerical simulations are performed to confirm the analytical results.
本文表明，在一对一维复 Ginzburg-Landau（CGL）系统中，扩散连接可以诱导振幅死亡。在耦合 CGL 系统中对空间均匀稳态的稳定性分析表明，在由无延迟连接耦合的一对相同的 CGL 系统中，振幅死亡永远不会发生，但在延迟连接的情况下可能会发生。此外，在具有零标称频率的耦合相同 CGL 系统中，振幅死亡永远不会发生。基于这些分析结果，我们提出了一种设计连接延迟时间和耦合强度的方法，以诱导空间鲁棒稳定，即对任何系统大小和任何边界条件都能稳定的稳态。数值模拟验证了分析结果。
