关于一类神经元系统的动力学分析

旨在对Caianiello型离散神经元模型进行分析，由于这种模型具有动态阈值，它能够更加贴切地模拟生物神经元。这种神经元模型恰为延迟动力系统。我们所采用的方法是李雅普诺夫直接方法。文中对各种不同情况得到了神经元系统平衡点的数量、位置的结果。对每一种情况，我们还分析了这些平衡点的动态性质，理论分析和计算机仿真表明该神经元可以具有各种不同的特性，如全局吸引性、局部吸引性、不稳定性或振荡。

Dynamics Analysis on a Class of Neuron System

The purpose of this paper is to analyze the Caianiello type discrete neuron dynamical system, which simulates the biological neuron more precisely since it has the dynamical thresholds. The model of this type neuron is just the delay dynamical systems. By using the Lyapunov direct method, we analyze the equilibrium points of the neuron. In this paper, we determine the number of the equilibrium points and the locations of them in different cases. For each case, dynamical properties of these equilibrium points are obtained. The theoretical and simulation results show many dynamical behaviors of this neuron system, such as global, local attractive property, unstable or oscillation.