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2012 The Dynamics of a Predator-Prey System with State-Dependent Feedback Control
Hunki Baek
Abstr. Appl. Anal. 2012: 1-17 (2012). DOI: 10.1155/2012/101386

Abstract

A Lotka-Volterra-type predator-prey system with state-dependent feedback control is investigated in both theoretical and numerical ways. Using the Poincaré map and the analogue of the Poincaré criterion, the sufficient conditions for the existence and stability of semitrivial periodic solutions and positive periodic solutions are obtained. In addition, we show that there is no positive periodic solution with period greater than and equal to three under some conditions. The qualitative analysis shows that the positive period-one solution bifurcates from the semitrivial solution through a fold bifurcation. Numerical simulations to substantiate our theoretical results are provided. Also, the bifurcation diagrams of solutions are illustrated by using the Poincaré map, and it is shown that the chaotic solutions take place via a cascade of period-doubling bifurcations.

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Hunki Baek. "The Dynamics of a Predator-Prey System with State-Dependent Feedback Control." Abstr. Appl. Anal. 2012 1 - 17, 2012. https://doi.org/10.1155/2012/101386

Information

Published: 2012
First available in Project Euclid: 14 December 2012

zbMATH: 1243.34061
MathSciNet: MR2879937
Digital Object Identifier: 10.1155/2012/101386

Rights: Copyright © 2012 Hindawi

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