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Permanence effect in a three-species food chain model. (English) Zbl 0834.92023
Summary: This paper treats a reaction-diffusion system which models the dynamics of three-species food chain interactions in ecology. A sufficient condition is given to ensure the existence of a positive steady-state solution in terms of the natural growth rates of the three species. Under the same circumstance, the reaction-diffusion system has a positive global attractor which indicates the permanence effect in the ecological model.

MSC:
92D40 Ecology
35K57 Reaction-diffusion equations
35J60 Nonlinear elliptic equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
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