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Dynamics of a Modified Predator-Prey System to allow for a Functional Response and Time Delay

Published online by Cambridge University Press:  19 October 2016

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@mail.xjtu.edu.cn (Y. Jiang)
*Corresponding author. Email addresses:wliu2015@163.com (W. Liu), yljiang@mail.xjtu.edu.cn (Y. Jiang)
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Abstract

A modified predator-prey system described by two differential equations and an algebraic equation is discussed. Formulae for determining the direction of a Hopf bifurcation and the stability of the bifurcating periodic solutions are derived differential-algebraic system theory, bifurcation theory and centre manifold theory. Numerical simulations illustrate the results, which includes quite complex dynamical behaviour.

Keywords

Predator-prey systemharvestingstabilitytime delayperiodic solutions

MSC classification

Secondary: 92D25: Population dynamics (general)
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 4 , November 2016 , pp. 384 - 399
Copyright
Copyright © Global-Science Press 2016 

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