数学物理学报(英文版) ›› 2003, Vol. 23 ›› Issue (2): 208-.

• 论文 • 上一篇    下一篇

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

 徐瑞, 陈兰荪,M.A.J. Chaplain   

  1. Department of Mathematics, Mechanical Engineering College, Shijiazhuang 050003, China
    Institute of Mathematics, Academia Sinica, Beijing 100080, China
  • 出版日期:2003-04-07 发布日期:2003-04-07

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

 XU Rui, CHEN Lan-Sun,M.A.J. Chaplain   

  1. Department of Mathematics, Mechanical Engineering College, Shijiazhuang 050003, China
    Institute of Mathematics, Academia Sinica, Beijing 100080, China
  • Online:2003-04-07 Published:2003-04-07

摘要:

A delayed n-species nonautonomous Lotka-Volterra type competitive system
without dominating instantaneous negative feedback is investigated. By means of a suitable
Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of
the positive solutions of the system. As a corollary, it is shown 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 delays are sufficiently
small.

关键词: Nonautonomous Lotka-Volterra competitive system, finite and infinite delay,global asymptotic stability, Lyapunov functional

Abstract:

A delayed n-species nonautonomous Lotka-Volterra type competitive system
without dominating instantaneous negative feedback is investigated. By means of a suitable
Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of
the positive solutions of the system. As a corollary, it is shown 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 delays are sufficiently
small.

Key words: Nonautonomous Lotka-Volterra competitive system, finite and infinite delay,global asymptotic stability, Lyapunov functional

中图分类号: 

  • 34D23