Novel Existence and Stability Criteria of Periodic Solutions for Impulsive Delayed Neural Networks Via Coefficient Integral Averages

Abstract In this paper, an impulsive neural network with periodic coefficients and delayed time is firstly given, then the existence, uniqueness and exponential stability problems of periodic solutions for this system are further investigated. By means of the characteristic equation of delayed differential equations and impulsive differential equations, an impulsive delayed differential inequality with novel conditions are constructed. It can be used as an impulsive comparison system to deal with the existence and exponential stability problems. By utilizing the impulsive comparison system, Lyapunov functions and the fixed point theorem, we obtain the periodic solution's existence and exponential stability criteria. Finally, one numerical example and its simulations are given to illustrate the effectiveness of the theoretical results.

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