Global asymptotic stability in a nonautonomous n-species lotka—volterra predator—prey system with infinite delays

Abstract

In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution 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 mean delays are sufficiently small.

Keywords:

• Infinte delay
• Global asymptotic stability
• Lyapunov functional

AMS Subject Classifications:

• 34D23
• 34K20
• 92D25

^aDepartment of Mathematics, Mechanical Engineering College, Shijiazhuang 050003, Hebei, P.R. China

^*Corresponding author.

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

^aDepartment of Mathematics, Mechanical Engineering College, Shijiazhuang 050003, Hebei, P.R. China

^*Corresponding author.

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

Notes

^aDepartment of Mathematics, Mechanical Engineering College, Shijiazhuang 050003, Hebei, P.R. China

^*Corresponding author.

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

^bDepartment of Mathematics, University of Dundee, Dundee, DD1 4HN, UK

Additional information

Notes on contributors

Xu Rui

1 *