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Tbilisi Mathematical Journal

Editor-in-Chief: Inassaridze, Hvedri

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.14

Open Access
Online
ISSN
1512-0139
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A Nonlinear Nonautonomous Delay Differential Inequality for Dissipativity of Lotka-Volterra Functional Differential Equations

Liguang Xu
  • Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou, 310023, PR China
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Danhua He
Published Online: 2014-09-29 | DOI: https://doi.org/10.2478/tmj-2014-0004

Abstract

In this paper, a Lotka-Volterra functional differential equation is considered. By establishing a nonlinear nonautonomous delay differential inequality and using a generalized Barbˇlat's lemma, we obtain some new sufficient conditions ensuring the dissipativity of the Lotka-Volterra functional differential equation.

MSC: 34K38; 34K25

Keywords: Lotka-Volterra functional differential equations; Nonlinear delay differential inequality; Dissipativity; Generalized Barbˇlat's lemma

References

  • [1] L.P. Wen, Y.X. Yu and W.S. Wang, Generalized Halanay inequalities for dissipativity of Volterra functional differential equations, J. Math. Anal. Appl. 347 (2008), 169-178.Google Scholar

  • [2] D.Y. Xu and L.G. Xu, New results for studying a certain class of nonlinear delay differential systems, IEEE Trans. Autom. Control 55 (2010), 1641-1645.Google Scholar

  • [3] L.P. Wen, W.S. Wang and Y.X. Yu, Dissipativity and asymptotic stability of nonlinear neutral delay integro-differential equations, Nonlinear Anal. 72 (2010), 1746-1754.Google Scholar

  • [4] H.J. Tian, Numerical and analytic dissipativity of the h-method for delay differential equations with a bounded variable lag, Int. J. Bifur. Chaos 14 (2004), 1839-1845.CrossrefGoogle Scholar

  • [5] S.Q. Gan, Dissipativity of linear θ-methods for integro-differential equations, Comput. Math. Appl. 52 (2006), 449-458.Google Scholar

  • [6] S.Q. Gan, Dissipativity of θ-methods for nonlinear Volterra delay-integro-differential equations, J. Comput. Appl. Math. 206 (2007), 898-907.Google Scholar

About the article

Received: 2012-08-03

Accepted: 2014-07-15

Published Online: 2014-09-29


The work is supported by National Natural Science Foundation of China (Grant No. 11101367) and the China Scholarship Council (Grant No. 201208330001).


Citation Information: Tbilisi Mathematical Journal, Volume 7, Issue 1, ISSN (Online) 1512-0139, DOI: https://doi.org/10.2478/tmj-2014-0004.

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© 2014 Liguang Xu and Danhua He. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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