磁通耦合神经元模型的稳定性及Hopf分岔分析

Stability and Hopf Bifurcation Analysis of Flux-Coupled Neuron Model

通过磁通耦合的方法将两个磁通神经元耦合,建立耦合神经元模型。首先,利用Routh-Hurwitz判据分析平衡点的稳定性,并计算该模型的唯一平衡点;其次,由Hopf分岔定理得到分岔解析解,并研究模型的分岔方向及分岔周期解的稳定性;最后,通过数值仿真模拟模型的动力学行为。结果表明,在一定参数范围内,随着耦合强度的增加,模型产生亚临界Hopf分岔,同时出现倒倍周期、加周期分岔现象和较多的周期窗口,且增加外界刺激电流可诱导尖峰放电。

Two magnetic flux neurons were coupled by magnetic flux coupling,and the coupled neuron model was established.Firstly,Routh-Hurwitz criterion was used to analyze the stability of the equilibrium point and calculate the unique equilibrium point of the model.Secondly,the analytic solution of bifurcation was obtained by Hopf theorem,and the bifurcation direction of the model and the stability of bifurcation periodic solution were studied.Finally,the dynamic behavior of the model was simulated by numerical simulation.The results show that,within a certain range of parameters,with the increase of the coupling strength,the model generates a sub-critical Hopf bifurcation,and at the same time,the phenomenon of inverted doubling cycle,plus cycle bifurcation and more periodic windows appear,and increasing the external stimulation current can induce the spike discharge.