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Article
Impulsive Differential Equations: Periodic Solutions and Applications
Automatica
  • Xiaodi Li
  • Martin Bohner, Missouri University of Science and Technology
  • Chuan-Kui Wang
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.

Department(s)
Mathematics and Statistics
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.
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
Document Type
Article - Journal
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2015 Elsevier, All rights reserved.
Publication Date
2-1-2015
Publication Date
01 Feb 2015
Citation Information
Xiaodi Li, Martin Bohner and Chuan-Kui Wang. "Impulsive Differential Equations: Periodic Solutions and Applications" Automatica Vol. 52 (2015) p. 173 - 178 ISSN: 0005-1098
Available at: http://works.bepress.com/martin-bohner/162/