# zbMATH — the first resource for mathematics

Nonexistence of limit cycles in a predator-prey system with a sigmoid functional response. (English) Zbl 0977.92019
Summary: We consider a predator-prey system with a sigmoid functional response of the form $$\varphi(x)=x^n/(a+x^n)$$, $$n>1$$. Following J. Sugie et al. [J. Math. Anal. Appl. 159, No. 1, 224-236 (1991; Zbl 0731.34042); Appl. Math. Lett. 9, No. 4, 85-90 (1996; Zbl 0865.34032)], by taking advantage of H.I. Freedman and J.W.-H. So’s theorem [Math. Biosci. 76, 69-86 (1985; Zbl 0572.92025)] we present a sufficient and necessary condition for the nonexistence of limit cycles of this system with $$n>1$$.

##### MSC:
 92D25 Population dynamics (general) 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 92D40 Ecology