A nonautonomous predator-prey system with stage structure and double time delays

Authors:
Jiaoyan Wang;Qishao Lu;Zhaosheng Feng
Affiliations:
School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;School of Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;Department of Mathematics, University of Texas-Pan American, Edinburg, TX 78539, USA
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 5
Cited 0

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Abstract

In the present paper we study a nonautonomous predator-prey model with stage structure and double time delays due to maturation time for both prey and predator. We assume that the immature and mature individuals of each species are divided by a fixed age, and the mature predator only attacks the immature prey. Based on some comparison arguments we discuss the permanence of the species. By virtue of the continuation theorem of coincidence degree theory, we prove the existence of positive periodic solution. By means of constructing an appropriate Lyapunov functional, we obtain sufficient conditions for the uniqueness and the global stability of positive periodic solution. Two examples are given to illustrate the feasibility of our main results.