双时滞神经网络模型分支性的数值逼近

Hopf Bifurcations in Numerical Approximation for a Neural Network Model with Two Delays

数值逼近是数值计算中的基本问题,对仿真算法的理论研究有重要意义.文章研究了一类重要的双时滞神经网络模型的Hopf分支的数值逼近问题.首先,将时滞差分方程表示为映射,然后利用离散动力系统的分支理论,给出了差分方程的Hopf分支存在的条件.得到了连续模型的Hopf分支与其数值逼近的关系.证明了当该模型在juu=(L,2,1=j)处有Hopf分支时,其数值逼近在相应的)(hj=uu(L,2,1=j)处产生Hopf分支.数值Hopf分支值与原连续系统的Hopf分支值之间满足)()(hOhjj+=uu.

Numerical approximation is a fundamental problem of numerical analysis that has an important role for the theory of simulation algorithm. The numerical approximation of a class neural network model with two delays is considered. First, the delay deference equation is written as a map, and then, employing the theories of bifurcation for discrete dynamical systems, the conditions to guarantee the existence of Hopf bifurcations for numerical approximation are given. The relation of Hopf bifurcations between the continuous and the discrete are obtained. We prove that when the continuous model has Hopf bifurcations at juu=(L,2,1=j), the numerical approximation also has Hopf bifurcations at )(hj=uu(L,2,1=j). The numerical Hopf bifurcating values and the continuous systems satisfy )()(hOhjj+=uu.