时滞BAM神经网络的数值逼近

Numerical approximation of an n-dimensional BAM neural network model with multi-delays

研究了一类重要的多时滞BAM神经网络模型的Hopf分支的数值逼近问题.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,证明了当步长充分小时,数值Hopf分支值逼近于原方程的Hopf分支值.

The numerical approximation of a class neural network models with two delays was studied. First, the delay deference equation was expressed as mapping. By employing the theories of bifurcation for discrete dynamical systems, the conditions to guarantee the existence of Hopf bifurcations for numerical approximation were obtained. The relation of Hopf bifurcations between the continuous and the discrete systems were obtained. It is proved that the numerical Hopf bifurcation values are approximate to those of the original equation.