时滞三元离散神经网络模型的稳定性与分岔分析

Stability and Bifurcation of a Three-dimension Discrete Neural Network Model with Delay

研究了一类时滞三元离散神经网络模型,讨论其九种不同的连接形式并且运用离散动力系统Hopf分支理论和扩展的Jury判据理论对模型的特征方程根的分布进行分析,研究了模型的平衡点的稳定性及其分支周期解的存在性.最后通过数值模拟验证了所得结果的正确性.

Nine different types of three-dimension discrete neural network model with delay is considered.We derive some sufficient and necessary conditions on the asymptotic stability of the zero solution.In addition,it is found that there exists a Hopf bifurcation when the parameter passes some critical values by using Extensional Jury Criterion.Finally,computer simulations are performed to support the theoretical predictions.