A predator-prey model with Ivlev’s functional response. (English) Zbl 0851.34030

Kooij, R. E.; Zegeling, A.

J. Math. Anal. Appl. 198, No. 2, 473-489 (1996).

The uniqueness of limit cycles is proved for a two-dimensional predator-prey system with a functional response of Ivlev type. The system of planar autonomous ODE’s is transformed to a Liénard system to which a modified theorem of Zhang is applied.

Reviewer: B.D.Sleeman (Leeds)

MSC:

34C05	Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
92D25	Population dynamics (general)

Keywords:

uniqueness of limit cycles; two-dimensional predator-prey system; functional response of Ivlev type; Liénard system