Impulsive differential equations: Periodic solutions and applications

This paper deals with the periodic solutions problem for impulsive differential equations. By using Lyapunov's second method and the contraction mapping principle, some conditions ensuring the existence and global attractiveness of unique periodic solutions are derived, which are given from impulsive control and impulsive perturbation points of view. As an application, the existence and global attractiveness of unique periodic solutions for Hopfield neural networks are discussed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed results. (C) 2014 Elsevier Ltd. All rights reserved.