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2015 Existence of Multiple Limit Cycles in a Predator-Prey Model with $\arctan(ax)$ as Functional Response
Gunog Seo, Gail S. K. Wolkowicz
Commun. Math. Anal. 18(1): 64-68 (2015).

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.

Citation

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Gunog Seo. Gail S. K. Wolkowicz. "Existence of Multiple Limit Cycles in a Predator-Prey Model with $\arctan(ax)$ as Functional Response." Commun. Math. Anal. 18 (1) 64 - 68, 2015.

Information

Published: 2015
First available in Project Euclid: 12 August 2015

zbMATH: 1320.92073
MathSciNet: MR3365174

Subjects:
Primary: 92D40

Rights: Copyright © 2015 Mathematical Research Publishers

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Vol.18 • No. 1 • 2015
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