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

Volume 12, Issue 6, pp 363--375 Publication Date: January 30, 2019       Article History
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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.

### Keywords

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

•  93Dxx
•  45Gxx
•  47H14

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