一类神经元模型的放电行为与同步研究

Study on Discharge Behavior and Synchronization for a Neuron Model

以磁通e-HR神经元模型为基础,基于理论分析与数值仿真相结合的方法,首先分析了磁通e-HR神经元模型的放电行为,发现该神经元模型存在隐藏的极限环吸引子.通过双参数分岔分析观察到,系统具有倍周期和无混沌伴随的加周期等典型的放电行为.设计了自适应同步控制器,研究了时滞对电突触耦合的磁通e-HR神经元模型达到同步的影响.当时滞和耦合强度取一定值时,给从系统施加非线性控制器,从系统在控制器作用下与主系统达到同步.

Based on the flux-e-HR neuron model,the discharge behavior of the flux-e-HR neuron model is analyzed by using theoretical analysis and numerical simulation,and the hidden limit cycle attractors are found.By two-parameter bifurcation analysis,we can observe the typical discharge phenomena,such as period doubling and period adding without chaos.In addition,the adaptive synchronization controllers are designed to study the effect of time delay on the synchronization of the flux e-HR neuron model with elec­trical synaptic coupling.If the time delay and coupling strength are given a certain value,the slave system added by a nonlinear control theory will synchronize with the master system.