Dissipativity and stability of a class of nonlinear multiple time delay integro-differential equations

Volume 12, Issue 6, pp 363--375 http://dx.doi.org/10.22436/jnsa.012.06.03

Publication Date: January 30, 2019 Submission Date: July 05, 2017 Revision Date: November 23, 2018 Accteptance Date: December 20, 2018

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Authors

Chaolong Zhang - College of Computational Science, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, P. R. China. Feiqi Deng - Systems Engineering Institute, South China University of Technology, Guangzhou, 510640, P. R. China. Haoyi Mo - School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, P. R. China. Hongwei Ren - School of computer and electronic information, Guangdong University of Petrochemical Technology, Maoming 525000, P. R. China.

Abstract

This paper is concerned with the dissipativity and stability of the theoretical solutions of a class of nonlinear multiple time delay integro-differential equations. At the first, we give a generalized Halanay inequality which plays an important role in the study of dissipativity and stability of integro-differential equations. Then, we apply the generalized Halanay inequality to the dissipativity and the stability the theoretical solution of delay integro-differential equations (or by small \(\epsilon\) perturbed) and some interesting results are obtained. Our results generalize a few previous known results. Finally, two examples are provided to demonstrated the effectiveness and advantage of the theoretical results.

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Keywords

• Delay integro-differential equations
• dynamical systems
• Halanay inequality
• dissipativity
• stability

MSC

•  93Dxx
•  45Gxx
•  47H14

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