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Ratio-dependent predator-prey models of interacting populations. (English) Zbl 1170.92027

Summary: Ratio-dependent predator-prey models are increasingly favored by both the theoretical and experimental ecologists as a more suitable alternative to describe predator-prey interactions when the predators hunt seriously. In this article, the classical A. D. Bazykin model [Mathematical biophysics of interacting populations. Moskva: Nauka (Russian) (1985; Zbl 0605.92015)] is modified with ratio-dependent functional response. Stability and bifurcation situations of the system are observed. Since the ratio-dependent model always has difficult dynamics in the vicinity of the origin, the analytical behavior of the system near the origin is studied completely.

It is found that paradox of enrichment can happen to this system under certain parameter values, although the functional response is ratio-dependent. The parametric space for Turing spatial structures is determined. We also conclude that competition among the predator population might be beneficial for predator species under certain circumstances. Finally, ecological interpretations of our results are presented in the discussion section.

MSC:
92D40Ecology
37N25Dynamical systems in biology
34D23Global stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
34D05Asymptotic stability of ODE
35Q80Appl. of PDE in areas other than physics (MSC2000)
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