Global asymptotic stability in n-species nonautonomous Lotka--Volterra competitive systems with infinite delays

  • Authors:

  • Rui Xu;M. A. J. Chaplain;Lansun Chen

  • Affiliations:

  • Department of Mathematics, Mechanical Engineering College, 97 Heping West Road, Shijiazhuang 050003, People's Republic of China;Department of Mathematics, University of Dundee, Dundee, UK DD1 4HN;Institute of Mathematics, Academia Sinica, Beijing, 100080, People's Republic of China

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2002

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Abstract

By means of Lyapunov functional, we have succeeded in establishing the global asymptotic stability of the positive solutions of a delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedbacks. As a corollary, we show that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the mean delays are sufficiently small.