神经网络属于复杂网络,因其可以描述各种真实的系统受到了大量学者的研究,而稳定性一直是复杂网络的重要问题,研究了一类脉冲神经网络的指数稳定性;建立一个含有分布时滞和脉冲的变系数广义 Halanay 不等式,它有 3 个特点:含有脉冲,可以用来证明不连续系统的稳定性;系数为变系数,对不等式 的系数要求更为宽松,应用更加广泛;时滞为分布时滞;利用新建立的广义 Halanay 不等式,结合 Banach 不动点理论,建立简单的 Lyapunov 函数,得到了使脉冲神经网络周期解的存在性和指数稳定性的充分条件,说明了在满足条件时,脉冲时滞神经网络存在惟一周期解,并且周期解指数稳定。
Neural network belongs to complex network, which is studied by many scholars because it can describe all kinds of real systems. Stability is always an important problem of complex network. This paper studies exponential stability of a class of impulsive neural network. In this paper, we establish a generalized Halanay inequality with variable coefficient with distributed delay and impulse. The inequality has three characteristics:it can prove the stability of discontinuous systems with impulse;the coefficient is variable coefficient, and the requirement for the coefficient of inequality is more relaxed, which is more widely used;time delay is distributed time delay. By using the new generalized Halanay inequality and Banach fixed point theory, a simple Lyapunov function is established, and a sufficient condition is obtained for the existence and exponential stability of periodic solutions of impulsive neural networks. It is shown that when the condition is satisfied, the impulsive delay neural networks have unique periodic solutions and the periodic solutions are exponentially stable.
雷 婷, 朱 双.变系数时滞脉冲方程周期解的指数稳定性研究[J].重庆工商大学学报（自然科学版）,2022,39(5):78-84
LEI Ting, ZHU Shuang. Exponential Stability of Periodic Solutions of Time-delay Impulsive Equations with Variable Coefficients[J]. Journal of Chongqing Technology and Business University(Natural Science Edition）,2022,39(5):78-84