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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 the effect of time-delay on the dynamic behavior of ANN model, a bi-directional associative memory neural network model with n + 1 neurons with multiple delays is considered. Taking the time delay in the model as a parameter, The global Hopf bifurcation of differential equations and the Bendixson periodic solution of ordinary differential equations do not exist. The sufficient conditions for the global existence of nontrivial periodic solutions of this model are given. This provides an important theoretical basis for the design and application of bidirectional associative memory neural networks Finally, an numerical simulation is carried out with an example, the simulation results show the validity of the conclusion.