Heteroclinic Bifurcation and Multistability in a Ratio-dependent Predator-Prey System with Michaelis-Menten Type Harvesting Rate
نویسندگان
چکیده
In this article, we study a ratiodependent predator-prey system where predator population is subjected to harvesting with MichaelisMenten type harvesting rate. We study the existence of heteroclinic bifurcations in an exploited predatorprey system by using Melnikov’s method. Our simulation results also show that the system may exhibit monostability, bistability and tristability depending on the initial values of the system populations and the harvesting effort. Keywords—predator-prey model, ratio-dependence, harvesting, Melnikov functions, heteroclinic bifurcation.
منابع مشابه
Heteroclinic Bifurcation in the Michaelis-Menten-Type Ratio-Dependent Predator-Prey System
The existence of a heteroclinic bifurcation for the Michaelis–Menten-type ratiodependent predator-prey system is rigorously established. Limit cycles related to the heteroclinic bifurcation are also discussed. It is shown that the heteroclinic bifurcation is characterized by the collision of a stable limit cycle with the origin, and the bifurcation triggers a catastrophic shift from the state o...
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تاریخ انتشار 2012