具有化学突触的神经元网络中的簇同步。

Cluster synchronization in networks of neurons with chemical synapses.

作者信息

Juang Jonq, Liang Yu-Hao

机构信息

Department of Applied Mathematics, and Center of Mathematics Modeling and Scientific Computing, National Chiao Tung University, Hsinchu, Taiwan and National Center for Theoretical Sciences, Hsinchu, Taiwan.

Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan.

出版信息

Chaos. 2014 Mar;24(1):013110. doi: 10.1063/1.4862484.

DOI:10.1063/1.4862484

PMID:24697372

Abstract

In this work, we study the cluster synchronization of chemically coupled and generally formulated networks which are allowed to be nonidentical. The sufficient condition for the existence of stably synchronous clusters is derived. Specifically, we only need to check the stability of the origins of m decoupled linear systems. Here, m is the number of subpopulations. Examples of nonidentical networks such as Hindmarsh-Rose (HR) neurons with various choices of parameters in different subpopulations, or HR neurons in one subpopulation and FitzHugh-Nagumo neurons in the other subpopulation are provided. Explicit threshold for the coupling strength that guarantees the stably cluster synchronization can be obtained.

摘要

在这项工作中，我们研究了化学耦合且一般形式的网络的簇同步，这些网络可以是非相同的。推导了稳定同步簇存在的充分条件。具体而言，我们只需要检查(m)个解耦线性系统原点的稳定性。这里，(m)是子群体的数量。给出了非相同网络的例子，比如在不同子群体中具有各种参数选择的 Hindmarsh-Rose（HR）神经元，或者一个子群体中的 HR 神经元和另一个子群体中的 FitzHugh-Nagumo 神经元。可以得到保证稳定簇同步的耦合强度的明确阈值。