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Global dynamics of a predator-prey model with Hassell-Varley type functional response. (English) Zbl 1160.34046
The authors present a systematic global qualitative analysis to a general predator-prey model with Hassell-Varley type functional response. The authors show that the predator free equilibrium is a global attractor only when the predator death rate is greater than its growth ability. The positive equilibrium exists if the above relation reverses. In cases of practical interest, authors show that the local stability of the positive steady state implies its global stability with respect to positive solutions. For terrestrial predators that form a fixed number of tight groups, authors show that the existence of an unstable positive equilibrium in the predator-prey model implies the existence of an unique nontrivial positive limit cycle.
MSC:
 34C60 Qualitative investigation and simulation of models (ODE) 34D05 Asymptotic stability of ODE 34D20 Stability of ODE 92D25 Population dynamics (general) 34C05 Location of integral curves, singular points, limit cycles (ODE) 34D23 Global stability of ODE