【摘要】 运用动力系统稳定性理论和分岔理论对两个全同三维神经元模型耦合得到的模型(简称耦合神经元模型)进行了研究.平衡点分析表明,对任意的耦合强度gs,耦合神经元模型总存在一个对称平衡点;当gs变化时,非对称平衡点成对出现或成对消失.分岔分析显示,耦合神经元模型会发生折分岔或Hopf分岔.第一李雅普诺夫系数表明系统发生的Hopf分岔是超临界的且极限环稳定.研究结果有助于探究高维耦合神经元模型的动力学行为.更多还原

【Abstract】 The coupled model of two identical three-dimensional neuron models( abbreviated as coupled neuron model) is studied with stability theory and bifurcation theory of the dynamic systems. The analysis of equilibrium point shows that there is a symmetric equilibrium point in the coupled neuron model for any coupling strength gs; when gschanges,the asymmetric equilibrium point appears or disappears in pairs. The bifurcation analysis shows that fold bifurcation or Hopf bifurcation can occur in the coupled neuron model. The first Lyapunov coefficient indicates that the Hopf bifurcation of the system is supercritical and the corresponding limit cycle is stable. The results of this study are helpful to explore the dynamic behavior of the high dimensional coupled neuron models.更多还原