Impulsive Differential Equations: Periodic Solutions and Applications
Abstract
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.
Recommended Citation
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
Department(s)
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)
0005-1098
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 Elsevier, All rights reserved.
Publication Date
01 Feb 2015
Comments
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.