两个同质动力学性态的Aihara神经元电突触耦合的完全同步

On Complete Synchronization of Two Identical Aihara Neurons Model via Electrical Synapse Coupling

讨论两个同质动力学性态下的Aihara神经元耦合系统的状态完全同步问题.以主稳定函数为分析工具,首先通过数值模拟指出单个神经元处于混沌放电状态时,神经元对应的最大Lyapunov指数具有非负的性质;其次,对于两个Aihara神经元在电突触耦合下构成的系统,给出系统能实现状态完全同步的一个必要条件,利用系统的主稳定函数值绘制了2维参数平面的完全同步区域.数值仿真表明,过大或过小的耦合强度都不能使耦合系统达到状态的完全同步.最后,所设计的数值实例表明了理论结果的合理性和有效性.

Complete synchronization of two identical dynamical Aihara neurons model has been discussed. Based on the Master Stability Function (MSF) analysis and numerical simulations, the property that the corresponding maximum Lyapunov exponents are non-negative has been presented firstly during the single neuron is in chaotic state. Secondly, a necessary condition for complete synchronization of two electrical coupled identical Aihara neurons has been given and the 2-dimensional parameter-space plot that displays the values of the MSF has been obtained numerically. The simulations show that complete synchronization cannot be reached if the coupling strength is taken too much or too few. Finally, reasonability and effectiveness of the theoretical results are verified by designed numerical examples.