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Dynamics of a stage-structured Leslie-Gower predator-prey model. (English) Zbl 1235.34194

Summary: A generalized version of the Leslie-Gower predator-prey model that incorporates the prey population structure is introduced. Our results show that the inclusion of (age) structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the “trapping” of the dynamics in a biological compact set-albeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results.

MSC:

34K20 Stability theory of functional-differential equations
37N25 Dynamical systems in biology
34K12 Growth, boundedness, comparison of solutions to functional-differential equations
92D25 Population dynamics (general)
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