Global Analysis of a Nonautonomous Predator-Prey Model with Double Delays and Stage Structure
Li Ying-ke *
College of Mathematics and Physics, Xinjiang Agriculture University, Urumqi 830052, P.R.C
Dena Turehan
College of Mathematics and Physics, Xinjiang Agriculture University, Urumqi 830052, P.R.C
Mehbuba Rehem
College of Mathematics and System Science, Xinjiang University, Urumqi 830046, P.R.C
*Author to whom correspondence should be addressed.
Abstract
A nonautonomous predator-prey system with stage-structure and double time delays is investigated in the present paper. Based on some comparison arguments we discuss the permanence of the species. By using the continuation theorem of coincidence degree theory, the existence of a positive periodic solution for the system is established. Further, by constructing a V functional and using the result of the existence of positive periodic solution, we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution.
Keywords: Predator-prey, Stage-structure, Continuation theorem, Periodic solutions, Global stability