Cluster synchronization in networks of neurons with chemical synapses.
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.
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.
Jonq
J
Juang
Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan.
Yu-Hao
YH
Liang
D000818:Animals; D006801:Humans; D008959:Models, Neurological; D009415:Nerve Net / Q000502:physiology*; D009474:Neurons / Q000502:physiology*; D013569:Synapses / Q000502:physiology*