Periodic solutions for a delayed predator-prey model of prey dispersal in two-patch environments. (English) Zbl 1066.92059

Summary: A delayed periodic Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments is investigated. By using R. E. Gaines and J. L. Mawhin’s [Coincidence degree and nonlinear differential equations. (1977; Zbl 0339.47031)] continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are obtained to guarantee the existence, uniqueness and global stability of positive periodic solutions of the system. Numerical simulations are given to illustrate the feasibility of our main results.


92D40 Ecology
34K13 Periodic solutions to functional-differential equations
37N25 Dynamical systems in biology
34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K20 Stability theory of functional-differential equations


Zbl 0339.47031
Full Text: DOI


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