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Nonlinear Dynamical Behaviour in a Predator-Prey Model with Harvesting

Published online by Cambridge University Press:  02 May 2017

Wei Liu  and
Yaolin Jiang
Wei Liu*
Affiliation:
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China School of Mathematics and Computer Science, Xinyu University, Xinyu 338004, China
Yaolin Jiang*
Affiliation:
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an 710049, China
*
*Corresponding author. Email addresses:wliu2015@163.com (W. Liu), yljiang@xjtu.edu.cn (Y.L. Jiang)
*Corresponding author. Email addresses:wliu2015@163.com (W. Liu), yljiang@xjtu.edu.cn (Y.L. Jiang)
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Abstract

We investigate the stability and periodic orbits of a predator-prey model with harvesting. The model has a biologically-meaningful interior, an attractor undergoing damped oscillations, and can become destabilised to produce periodic orbits via a Hopf bifurcation. Some sufficient conditions for the existence of the Hopf bifurcation are established, and a stability analysis for the periodic solutions using a Lyapunov function is presented. Finally, some computer simulations illustrate our theoretical results.

Keywords

Predator-prey systemHolling type IV functional responseperiodic solutionbifurcationLyapunov function

MSC classification

Secondary: 92D25: Population dynamics (general)
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 376 - 395
Copyright
Copyright © Global-Science Press 2017 

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