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.
X. Li et al., "Impulsive Differential Equations: Periodic Solutions and Applications," Automatica, vol. 52, pp. 173 - 178, Elsevier, Feb 2015.
The definitive version is available at https://doi.org/10.1016/j.automatica.2014.11.009
Mathematics and Statistics
Keywords and Phrases
Banach spaces; Differential equations; Mapping; Attractiveness; Contraction Mapping principles; Existence; Global attractiveness; Impulsive controls; Impulsive differential equation; Impulsive perturbations; Periodic solution; Hopfield neural networks; Attractiveness; Contraction mapping principle; Existence; Hopfield neural networks; Impulsive differential equations; Lyapunov's second method
International Standard Serial Number (ISSN)
Article - Journal
© 2015 Elsevier, All rights reserved.
01 Feb 2015
This work was jointly supported by National Natural Science Foundation of China (No. 11301308), China Postdoctoral Science Foundation founded project (2014M561956) and Research Fund for International Cooperation Training Programme of Excellent Young Teachers of Shandong Normal University.