Bifurcations analysis of Leslie-Gower predator-prey models with nonlinear predator-harvesting
Open Access
- 1 January 2017
- journal article
- Published by American Institute of Mathematical Sciences (AIMS) in Discrete and Continuous Dynamical Systems - S
- Vol. 10 (5) , 1187-1206
Abstract
In the present paper the dynamics of a Leslie-Gower predator-prey model with Michaelis-Menten type predator harvesting is studied. We give out all the possible ranges of parameters for which the model has up to five equilibria. We prove that these equilibria can be topological saddles, nodes, foci, centers, saddle-nodes, cusps of codimension 2 or 3. Numerous kinds of bifurcations also occur, such as the transcritical bifurcation, pitchfork bifurcation, Bogdanov-Takens bifurcation and homoclinic bifurcation. Several numerical simulations are carried out to illustrate the validity of our results.Keywords
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