具有时滞磁通神经元模型的Hopf分岔分析

Hopf Bifurcation Analysis of Flux Neuron Model with Time Delays

利用稳定性理论和中心流形定理等方法研究双时滞磁通神经元模型的稳定性、Hopf分岔的存在性以及分岔方向和分岔周期解的稳定性,并给出部分数值模拟验证所得结论.结果表明:在特定时滞范围内模型存在分岔周期解;时滞的增加可诱导尖峰放电行为.

We studied the stability,the existence of Hopf bifurcation and the stability bifurcation direction and bifurcation periodic solution of the double-delay flux neuron model by using stability theory,central manifold theorem and other methods,and some conclusions obtained by numerical simulation were given.The results show that the bifurcation periodic solution of the model is obtained within a certain time delay range,and the increase of time delay can induce the spike discharge behavior.