BIFURCATION-ANALYSIS OF A NEURAL NETWORK MODEL
BIFURCATION-ANALYSIS OF A NEURAL NETWORK MODEL
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DOI：
10.1007/bf00203668
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发表时间：
1992-02-01
影响因子：
1.9
通讯作者：
KIRILLOV, AB
中科院分区：
文献类型：
--
作者：
BORISYUK, RM;KIRILLOV, AB
本文描述了Wilson和Cowan对著名的神经网络模型的分析。神经网络由描述兴奋性和抑制性神经元群体平均活动演化的两个常微分方程组组成。分析了模型的行为对两个参数的依赖关系。将参数平面划分为以分叉曲线为边界的等价行为区域，并为每个区域构造代表相图。这使我们能够定性地描述模型在每个区域中的行为，并预测随着参数的变化模型动态的变化。特别地，我们证明了对于某些参数值，系统可以表现出长周期振荡。当系统根据初始点稳定到定常态或极限环时，还发现了一种新的动力学行为。
This paper describes the analysis of the well known neural network model by Wilson and Cowan. The neural network is modeled by a system of two ordinary differential equations that describe the evolution of average activities of excitatory and inhibitory populations of neurons. We analyze the dependence of the model's behavior on two parameters. The parameter plane is partitioned into regions of equivalent behavior bounded by bifurcation curves, and the representative phase diagram is constructed for each region. This allows us to describe qualitatively the behavior of the model in each region and to predict changes in the model dynamics as parameters are varied. In particular, we show that for some parameter values the system can exhibit long-period oscillations. A new type of dynamical behavior is also found when the system settles down either to a stationary state or to a limit cycle depending on the initial point.