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Existence and global attractivity of positive periodic solutions for a predator-prey model with modified Leslie-Gower Holling-type II schemes. (English) Zbl 1232.34077
The authors investigate a periodic predator-prey model whose functional responses are of Holling-type II. Their aim is to find easily verifiable sufficient conditions for the existence and global attractivity of a periodic solution in the positive quadrant. To prove their results, they derive a-priori estimates for such solutions, make use of the coincidence degree for Fredholm operators of index zero, and, moreover, find an appropriate Lyapunov function. A simple numerical example concludes the paper.

MSC:
34C60 Qualitative investigation and simulation of ordinary differential equation models
92D25 Population dynamics (general)
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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