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Dynamic analysis of a delayed reaction-diffusion predator-prey system with modified Holling-Tanner functional response. (English) Zbl 1344.92143

Summary: A predator-prey model with modified Holling-Tanner functional response and time delays is considered. By regarding the delays as bifurcation parameters, the local and global asymptotic stability of the positive equilibrium are investigated. The system has been found to undergo a Hopf bifurcation at the positive equilibrium when the delays cross through a sequence of critical values. In addition, the direction of the Hopf bifurcation and the stability of bifurcated periodic solutions are also studied, and an explicit algorithm is obtained by applying normal form theory and the center manifold theorem. The main results are illustrated by numerical simulations.

MSC:

92D25 Population dynamics (general)
34D20 Stability of solutions to ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
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