DYNAMICS OF RATIO-DEPENDENT PREDATOR-PREY MODELS WITH NONCONSTANT HARVESTING

被引：48
|
作者：
Leard, Benjamin [1 ]
Lewis, Catherine [2 ]
Rebaza, Jorge [3 ]
机构：
[1] James Madison Univ, Dept Math & Stat, Harrisonburg, VA 22807 USA
[2] Whitman Coll, Math Dept, Walla Walla, WA 99362 USA
[3] Missouri State Univ, Dept Math, Springfield, MO 65897 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2008年 / 1卷 / 02期
关键词：
Dynamical systems; predator-prey models; harvesting;
D O I：
10.3934/dcdss.2008.1.303
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：303 / 315
页数：13
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