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June  2008, 1(2): 303-315. doi: 10.3934/dcdss.2008.1.303

Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting

Benjamin Leard 1, , Catherine Lewis 2, and  Jorge Rebaza 3,

1. 

Department of Mathematics and Statistics, James Madison University, Harrisonburg, Virginia 22807, United States
2. 

Mathematics Department, Whitman College, Walla Walla, WA 99362, United States
3. 

Department of Mathematics, Missouri State University, Springfield, MO 65897, United States

Received  October 2007 Revised  November 2007 Published  March 2008

The dynamics of constant harvesting of a single species has been studied extensively within the framework of ratio-dependent predator-prey models. In this work, we investigate the properties of a Michaelis-Menten ratio-dependent predator-prey model with two nonconstant harvesting functions depending on the prey population. Equilibria and periodic orbits are computed and their stability properties are analyzed. Several bifurcations are detected as well as connecting orbits, with an emphasis on analyzing the equilibrium points at which the species coexist. Smooth numerical continuation is performed that allows computation of branches of solutions.
Keywords: harvesting., predator-prey models, Dynamical systems.
Mathematics Subject Classification: Primary: 37N25; Secondary: 65L9.
Citation: Benjamin Leard, Catherine Lewis, Jorge Rebaza. Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 303-315. doi: 10.3934/dcdss.2008.1.303
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