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• W2740653460 abstract "Abstract—In this article, we study a ratio-dependent predator-prey system where predator pop-ulation is subjected to harvesting with Michaelis-Menten type harvesting rate. We study the existenceof heteroclinic bifurcations in an exploited predator-prey system by using Melnikov’s method. Our simu-lation results also show that the system may exhibitmonostability, bistability and tristability dependingon the initial values of the system populations andthe harvesting effort.Keywords—predator-prey model, ratio-dependence,harvesting, Melnikov functions, heteroclinic bifurca-tion. 1 Introduction The standard Lotka-voltera type models assume that the per-capita rate of predation depends on the prey numbers only.This means that the predator’s functional response is a func-tion of prey density only. In general, predator’s functional re-sponse should certainly be a function of both prey and preda-tor densities [1, 2] as there is often competition among thepredators for their food. A simple alternative assumption isthat the per capita rate of predation depends on the ratio ofprey to predator densities.It is well known that classical prey-dependent predator preymodel exhibits the ”paradox of enrichment” [3, 4] which statesthat enriching a predator prey system (by increasing the car-rying capacity) will cause an increase in the equilibrium den-sity of the predator but not in that of prey and will destabilizethe positive equilibrium, and thus increases the possibilitiesof the stochastic extinction of the predator. However, nu-merus field observations provide contrary to this paradox ofenrichment. It is often observed in nature that fertilizationincreases the prey density, but does not destabilize a stablesteady state and fails to increase the amplitude of the os-" @default.
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• W2740653460 date "2012-01-01" @default.
• W2740653460 modified "2023-09-27" @default.
• W2740653460 title "Heteroclinic Bifurcation and Multistability in a Ratio-dependent Predator-Prey System with Michaelis-Menten Type Harvesting Rate" @default.
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