脉冲干扰时滞复值神经网络的稳定性分析

摘要

为分析脉冲干扰因素对复值神经网络动态行为的影响,研究一类具有混合时滞和脉冲干扰的复值神经网络的平衡点的全局指数稳定性.在假定神经元状态、激活函数以及关联矩阵定义在复数域的情况下,利用M矩阵理论、向量Lyapunov函数法以及数学归纳法,分析确保该系统平衡点的存在性、唯一性以及全局指数稳定性的充分条件,并给出了指数收敛率,最后通过一个数值仿真算例验证了所得结论的正确性.结果表明:时滞和脉冲干扰均会降低神经元状态的指数收敛速度,所建立的稳定性判据推广了现有结论.%To investigate the effect of impulsive disturbances on the dynamical behavior of the equilibrium point of complex-valued neural networks, the globally exponential stability of a class of the system with mixed delays and impulsive disturbances was studied in this paper. Assume that the neuron states, activation functions and interconnected matrix were defined in the complex domain. Some sufficient conditions for assuring the existence, uniqueness and globally exponential stability of the equilibrium point of the system were obtained by applying the M matrix theory, the mathematical induction and the vector Lyapunov function methods. Meanwhile, the exponential convergence rate was proposed. It can be concluded from the established sufficient conditions that the exponential convergence rate of the neurons is reduced by both time delays and the impulsive disturbances. The stability criteria established in this paper generalize the existing results. Finally, a numerical example with simulations was given to show the correctness of the obtained results.