BIFURCATIONS OF A HOLLING-TYPE II PREDATOR–PREY SYSTEM WITH CONSTANT RATE HARVESTING-Reference-Cited by-同舟云学术

BIFURCATIONS OF A HOLLING-TYPE II PREDATOR–PREY SYSTEM WITH CONSTANT RATE HARVESTING

Published:2009-08 Issue:08 Volume:19 Page:2499-2514
ISSN:0218-1274
Container-title:International Journal of Bifurcation and Chaos
language:en
Short-container-title:Int. J. Bifurcation Chaos

Author:

PENG GUOJUN¹,JIANG YAOLIN¹,LI CHANGPIN²

Affiliation:

1. Department of Mathematics, Xi'an Jiao Tong University, Xi'an 710049, P. R. China

2. Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China

Abstract

The objective of this paper is to study the dynamical properties of a Holling-type II predator–prey system with constant rate harvesting. It is shown that the model has at most three equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the degenerate Bogdanov–Takens bifurcation of codimension 3, the supercritical and subcritical Hopf bifurcation, the generalized Hopf bifurcation. These results reveal far richer dynamics than that of the model with no harvesting.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

Link

https://www.worldscientific.com/doi/pdf/10.1142/S021812740902427X

Reference16 articles.

1. Geometrical Methods in the Theory of Ordinary Differential Equations

2. Stability regions in predator-prey systems with constant-rate prey harvesting

3. Normal Forms and Bifurcation of Planar Vector Fields

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