Bifurcations of a Ratio-Dependent Holling-Tanner System with Refuge and Constant Harvesting
Xia LiuCollege of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, ChinaY̱epeng XingCollege of Mathematics and Science, Shanghai Normal University, Shanghai 200234, China
2013en
ABI
Abstract
The bifurcation properties of a predator prey system with refuge and constant harvesting are investigated. The number of the equilibria and the properties of the system will change due to refuge and harvesting, which leads to the occurrence of several kinds bifurcation phenomena, for example, the saddle-node bifurcation, Bogdanov-Takens bifurcation, Hopf bifurcation, backward bifurcation, separatrix connecting a saddle-node and a saddle bifurcation and heteroclinic bifurcation, and so forth. Our main results reveal much richer dynamics of the system compared to the system with no refuge and harvesting.
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