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Dynamics of a modified Holling-Tanner predator-prey model with diffusion. (English) Zbl 1429.35133

Summary: In this paper, we study the asymptotic behavior and Hopf bifurcation of the modified Holling-Tanner models for the predator-prey interactions in the absence of diffusion. Further the direction of Hopf bifurcation and stability of bifurcating periodic solutions are investigated. Diffusion driven instability of the positive equilibrium solutions and Turing instability region regarding the parameters are established. Finally we illustrate the theoretical results with some numerical examples.

MSC:

35K57 Reaction-diffusion equations
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92B05 General biology and biomathematics
92D25 Population dynamics (general)
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