A Nonlinear Nonautonomous Delay Differential Inequality for Dissipativity of Lotka-Volterra Functional Differential Equations

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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.


  • [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.

  • [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.

  • [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.

  • [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.

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

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