Geodesic
Dissipativity and stability of a class of nonlinear multiple time delay integro-differential equations
Zhang, Chaolong 1 ; Deng, Feiqi 2 ; Mo, Haoyi 3 ; Ren, Hongwei 4
1 College of Computational Science, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, P. R. China
2 Systems Engineering Institute, South China University of Technology, Guangzhou, 510640, P. R. China
3 School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, P. R. China
4 School of computer and electronic information, Guangdong University of Petrochemical Technology, Maoming 525000, P. R. China
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 363-375.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.012.06.03
Classification : 93Dxx, 45Gxx, 47H14
Keywords: Delay integro-differential equations, dynamical systems, Halanay inequality, dissipativity, stability

Zhang, Chaolong  1 ; Deng, Feiqi  2 ; Mo, Haoyi  3 ; Ren, Hongwei  4

1 College of Computational Science, Zhongkai University of Agriculture and Engineering, Guangzhou, 510225, P. R. China
2 Systems Engineering Institute, South China University of Technology, Guangzhou, 510640, P. R. China
3 School of Applied Mathematics, Guangdong University of Technology, Guangzhou, 510006, P. R. China
4 School of computer and electronic information, Guangdong University of Petrochemical Technology, Maoming 525000, P. R. China 
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Zhang, Chaolong ; Deng, Feiqi ; Mo, Haoyi ; Ren, Hongwei . Dissipativity and stability of a class of nonlinear multiple time delay integro-differential equations. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 6, p. 363-375. doi : 10.22436/jnsa.012.06.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.06.03/

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