Global dynamics of a predator-prey model with Hassell-Varley type functional response. (English) Zbl 1160.34046

Hsu, Sze-Bi; Hwang, Tzy-Wei; Kuang, Yang

Discrete Contin. Dyn. Syst., Ser. B 10, No. 4, 857-871 (2008).

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.

Reviewer: Xinyu Song (Xinyang)

MSC:

34C60	Qualitative investigation and simulation of ordinary differential equation models
34D05	Asymptotic properties of solutions to ordinary differential equations
34D20	Stability of solutions to ordinary differential equations
92D25	Population dynamics (general)
34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34D23	Global stability of solutions to ordinary differential equations

Keywords:

functional response; predator-prey model; global stability; limit cycles; extinction