三元离散神经网络模型的稳定性与分岔

Stability and bifurcation of a three-dimension discrete neural network model

研究一类三元神经网络模型。运用离散动力系统Hopf分支理论和扩展的July判据理论对该模型的特征方程根的分布进行分析,研究该模型的平衡点的稳定性和分岔,利用中心流形定理和正规形方法,给出确定分支周期解的分支方向与稳定性的计算公式。数值模拟验证了所得结果的正确性。

A Three-dimension discrete neural network model is considered.The linear stability of the model is studied.It is found that there exists Hopf bifurcations when the parameter passes a sequence of critical values.Using the normal form method and the center manifold theorem,the explicit formulas which determine the direction of the Hopf bifurcations and the stability of bifurcating periodic solutions are derived.Finally,computer simulations are performed to support the theoretical predict.