一种基于旋转变换的Morris-Lecar神经元模型的动力学特性分析

Dynamical Characteristics Analysis of Morris-Lecar Neuron Model with Rotational Transformation

为了使神经元模型能表现出丰富的放电特性,对三维Morris-Lecar神经元系统施加旋转变换,计算不同旋转角度下的平衡点及其对应特征值,利用分岔图、相图和时间历程图研究混沌振荡,并与偏置控制进行对比分析.数值结果表明含有旋转变换的Morris-Lecar神经元模型不仅能保持平衡点的稳定性,而且也不需要任何耦合项就能实现对吸引子相位的控制.

In order to enable the neuron model to exhibit rich discharge properties,a rotational transformation is applied to the three-dimensional Morris-Lecar neuron system,the equilibrium points and their corresponding eigenvalues are computed for different rotation angles,and chaotic oscillations are investigated by using bifurcation diagrams,phase diagrams,and time-course diagrams,and are analyzed in comparison with bias control.The numerical results show that the Morris-Lecar neuron model containing the rotational transformation not only maintains the stability of the equilibrium point,but also realizes the control of the attractor phase without any coupling term.