Stationary oscillation of an impulsive delayed system and its application to chaotic neural networks

Abstract

This paper investigates the stationary oscillation for an impulsive delayed system which represents a class of nonlinear hybrid systems. First, a new concept of S-stability is introduced for nonlinear impulsive delayed systems. Based on this new concept and fixed point theorem, the relationship between S-stability and stationary oscillation (i.e., existence, uniqueness and global stability of periodic solutions) for the nonlinear impulsive delayed system is explored. It is shown that the nonlinear impulsive delayed system has a stationary oscillation if the system is S-stable. Second, an easily verifiable sufficient condition is then obtained for stationary oscillations of nonautonomous neural networks with both time delays and impulses by using the new criterion. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed method.