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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:
34C60Qualitative investigation and simulation of models (ODE)
92D25Population dynamics (general)
34C25Periodic solutions of ODE
34D23Global stability of ODE
47N20Applications of operator theory to differential and integral equations
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