为了研究时滞对联想记忆神经网络模型动力学行为的影响,考虑了一个含有n+1个神经元的具多时滞的双向联想记忆神经网络模型.以模型中的时滞为参数,利用泛函微分方程的全局Hopf分支存在定理和常微分方程的Bendixson周期解不存在定理,给出该模型非平凡周期解全局存在的充分条件,为双向联想记忆神经网络的设计和应用提供了重要的理论依据.最后利用一个例子进行了数值仿真,仿真结果表明了结论的有效性.
In order to study for the effect of delay in dynamic behavior of associative memory neural net- work model, an n+l-dimensional bidirectional associative memory (BAM) neural network model with multi- delay was considered. Sufficient conditions for nontrivial periodic solution were met by the model by taking de- lay as a parameter, using the global Hopf bifurcation existence theorem of the functional differential equation and the Bendixson non-existent theorem of the ordinary differential equation. These provide important theoreti- cal basis for the design and application of BAM neural network. Finally, numerical simulations were carried out and results show that the proposed conclusion is effective.