神经元耦合系统同步条件的几点注记

研究了2个双向电突触耦合的完全相同的Hindmarsh-Rose神经元模型的完全同步问题.电突触耦合是神经元之间用于通讯的主要方式之一,它的最大功能是使神经元集群发生同步放电活动.以往对于耦合神经系统同步的研究,大多是利用数值方法,缺乏确凿的理论依据,对于多个神经元耦合的情形,也没有有效的方法.提出了2种判断完全同步的新方法——李雅普诺夫函数法和模式分解法,与传统的条件李雅普诺夫指数方法只能给出完全同步发生的必要条件相比,得到同步发生的充要条件和充分条件,并给出严格的理论证明.方法可应用到多个振子耦合和非对称耦合的系统中.计算机数值模拟对方法的有效性进行了验证. 

Some notes on complete synchronization of the coupled neurons

Complete synchronization of two mutually coupled identical chaotic Hindmarsh-Rose neurons model with gap junction was studied.Gap junction is also called electrical coupling,it acts as one of the main communications between neurons in nervous systems,its most important role is to make a large ensembles of neurons emit synchronous firing rhythm patterns.The traditional method to investigate complete synchronization was using numerical simulations,such as the conditional Lyapunov exponents,but it was lack of theoretical foundation and can only offer us a necessary condition to guarantee the occurrence of complete synchronization.Based on the conditional Lyapunov exponents method,synchronization of more coupled neurons is hard to be studied.So two new methods of Lyapunov function method and mode decomposition method here was introduced,and if and only if condition and the sufficient condition will be given.These methods are efficient to deal with more coupled neurons and nonsymmetrical coupling schemes,the validity of them was tested by numerical simulation.