复杂网络上的部分同步化:奇异态、遥同步与集团同步

Partial synchronization in complex networks: Chimera state,remote synchronization, and cluster synchronization

近年来,复杂网络上耦合振子的部分同步化引起了人们极大的关注,其潜在或背后的原因是部分同步化斑图在大脑网络中广泛存在,并很可能与大脑的认知或记忆等功能有密切的联系.本文对这些进展进行简单的总结与归纳,并按照学者们研究的不同侧重点,将其分成三方面来进行介绍,即奇异态、遥同步与集团同步化.着重强调这三种情形各自出现的条件、常用的研究模型、检测的方法以及侧重解释的生物现象等方面.并对它们三者之间的相互关系及今后的研究方向做一些简单的探讨.

In recent years, the study of partial synchronization of coupled oscillators in complex networks has attracted great attention. The underlying reason is both the extensive existence of the patterns of partial synchronization in brain network and their close relationship to brain functions of cognition and memory. In this paper, we briefly review the research progress in this field. According to the researches by different groups,we classify them as three types, i.e. chimera state, remote synchronization, and clustering synchronization. We mainly discuss the conditions of these three states, as well as their models, detections, and their applications in biology. We discuss the relationship among the three types of states and give some outlooks for future studies.