一类混合时滞复值神经网络的动态行为分析

Dynamic Behaviors Analysis of a Class of Complex-Valued Neural Networks with Mixed Time Delays

为将复值神经网络应用于模式识别,对一类具有混合时滞的复值神经网络平衡点的动态行为进行了探讨.在假定激活函数满足Lipschitz条件的情况下,利用同胚映射相关引理以及向量Lyapunov函数法,研究了确保该系统平衡点的存在性、唯一性以及指数稳定性的充分条件.研究结果表明,用复值神经网络的权系数、自反馈函数及激活函数所构造的判定矩阵是M矩阵.最后,通过一个数值仿真算例验证了所得结论的正确性.

To apply the complex-valued neural networks to pattern recognition, the dynamical behaviors of the equilibrium point of a class of complex-valued networks with mixed time delays were investigated. Assuming that the activation functions satisfy the global Lipschitz condition, some sufficient conditions for assuring the existence, uniqueness and exponential stability of the equilibrium point of the system were obtained by using homeomorphism mapping lemma and the vector Lyapunov function methods. The results show that the judgment matrices constructed using weighted coefficients, self-feedback functions and activation functions of the system were M matrix. Finally, a numerical example was presented to show the correctness of the obtained results.