Yanchuk Serhiy, Wolfrum Matthias
Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, 10117 Berlin, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Feb;77(2 Pt 2):026212. doi: 10.1103/PhysRevE.77.026212. Epub 2008 Feb 15.
We describe the mechanism of destabilization in a chain of identical coupled oscillators. Along with the transition from stationary to oscillatory behavior of the single oscillator, the network undergoes a complicated bifurcation scenario including the coexistence of multiple periodic orbits with different frequencies, spatial patterns, and modulation instabilities. This scenario, which is similar to the well-known Eckhaus scenario in spatially extended systems, occurs here also in the case of purely convective unidirectional coupling, and hence it cannot be explained as a simple discretization of its spatially continuous counterpart. Although the number of coexisting periodic orbits grows with the number of oscillators, we are able to treat this problem independently of the actual size of the network by investigating the limiting equations for the related spectral problems.
我们描述了由相同耦合振子组成的链中失稳的机制。随着单个振子从静止行为转变为振荡行为，网络经历了一个复杂的分岔过程，包括具有不同频率、空间模式和调制不稳定性的多个周期轨道的共存。这种情况类似于空间扩展系统中著名的埃克豪斯情况，在纯对流单向耦合的情况下也会出现，因此不能简单地将其解释为其空间连续对应物的离散化。尽管共存周期轨道的数量随着振子数量的增加而增加，但我们能够通过研究相关谱问题的极限方程，独立于网络的实际规模来处理这个问题。
