Communications in Mathematical Analysis

Existence of Multiple Limit Cycles in a Predator-Prey Model with $\arctan(ax)$ as Functional Response

Gunog Seo and Gail S. K. Wolkowicz

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Abstract

We consider a Gause type predator-prey system with functional response given by $θ(x)=\arctan(ax), where $a \gt 0$, and give a counterexample to the criterion given in Attili and Mallak [Commun. Math. Anal. 1:33-40(2006)] for the nonexistence of limit cycles. When this criterion is satisfied, instead this system can have a locally asymptotically stable coexistence equilibrium surrounded by at least two limit cycles.

Article information

Source
Commun. Math. Anal., Volume 18, Number 1 (2015), 64-68.

Dates
First available in Project Euclid: 12 August 2015

Permanent link to this document
https://projecteuclid.org/euclid.cma/1439384428

Mathematical Reviews number (MathSciNet)
MR3365174

Zentralblatt MATH identifier
1320.92073

Subjects
Primary: 92D40: Ecology

Keywords
Predatory–prey system multiple limit cycles functional response subcritical Hopf bifurcation

Citation

Seo, Gunog; Wolkowicz, Gail S. K. Existence of Multiple Limit Cycles in a Predator-Prey Model with $\arctan(ax)$ as Functional Response. Commun. Math. Anal. 18 (2015), no. 1, 64--68. https://projecteuclid.org/euclid.cma/1439384428


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