Various oscillation patterns in phase models with locally attractive and globally repulsive couplings
Various oscillation patterns in phase models with locally attractive and globally repulsive couplings
复制标题
具有局部吸引和全局排斥耦合的相位模型中的各种振荡模式
DOI：
10.1103/physreve.92.042922
复制
发表时间：
2015
影响因子：
2.4
通讯作者：
Katsuhiko Sato and Shin-ichiro Shima
中科院分区：
文献类型：
--
作者：
Koutaro Nakagome;Katsuhiko Sato;Seine A. Shintani;Shin’ichi Ishiwata;Katsuhiko Sato and Shin-ichiro Shima
我们研究了一个在一维空间中同时包含局部吸引和全局排斥耦合的相模型。这个模型表现出非平凡的时空模式，还没有观察到的系统，只包含本地或全球耦合。根据局部和全局耦合的相对强度以及全局耦合的形式，系统可以表现出空间均匀状态（同相同步）、单调递增状态（行波）和三种类型的相对相位差振荡。相对相位差的振荡具有局部不稳定但全局吸引的特性。也就是说，对相空间中周期轨道的任何微小扰动都会破坏其周期运动，但经过很长时间后系统又会恢复到原来的周期轨道。这一行为与鞍形两团簇态的出现密切相关，鞍形两团簇态通过吸引异宿轨道相互连接。讨论了这种振荡的发生机理。
We investigate a phase model that includes both locally attractive and globally repulsive coupling in one dimension. This model exhibits nontrivial spatiotemporal patterns that have not been observed in systems that contain only local or global coupling. Depending on the relative strengths of the local and global coupling and on the form of global coupling, the system can show a spatially uniform state (in-phase synchronization), a monotonically increasing state (traveling wave), and three types of oscillations of relative phase difference. One of the oscillations of relative phase difference has the characteristic of being locally unstable but globally attractive. That is, any small perturbation to the periodic orbit in phase space destroys its periodic motion, but after a long time the system returns to the original periodic orbit. This behavior is closely related to the emergence of saddle two-cluster states for global coupling only, which are connected to each other by attractive heteroclinic orbits. The mechanism of occurrence of this type of oscillation is discussed.