Abstract
By using Schaeffer′s theorem and Lyapunov functional, sufficient conditions of the existence and globally exponential stability of positive periodic solution to an impulsive neural network with time‐varying delays are established. Applications, examples, and numerical analysis are given to illustrate the effectiveness of the main results.
Highlights
It is well known that in implementation of neural networks, time delays are inevitably encountered because of the finite switching speed of amplifiers
By Lemma 2.3, it is easy to see that the existence of ω-periodic solution of 1.2 is equivalent to the existence of fixed point of the mapping φ in PC 0, ω, Rn
Let x∗ t be an ω-periodic solution of system 1.2 with initial value φ∗
Summary
It is well known that in implementation of neural networks, time delays are inevitably encountered because of the finite switching speed of amplifiers. The study of the existence of periodic solutions of neural networks has received much attention. Tan 1 considered the following neural network with variable coefficients and time-varying delays:. By using the Mawhin continuation theorem, they discussed the existence and globally exponential stability of periodic solutions. In this paper, by using Schaeffer’s theorem and Lyapunov functional, we aim to discuss the existence and exponential stability of periodic solutions to a class of impulsive neural networks with periodic coefficients and time-varying delays.
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