Period Doubling Cascades in a Predator-Prey Model with a Scavenger

被引：40

作者：

Previte, Joseph P. ^{[1
]}

Hoffman, Kathleen A. ^{[2
]}

机构：

[1] Penn State Univ, Behrend Coll, Sch Sci, Erie, PA 16563 USA

[2] UMBC, Dept Math & Stat, Baltimore, MD 21250 USA

来源：

SIAM REVIEW | 2013年 / 55卷 / 03期

关键词：

cascades; scavenger; bistability; Lotka-Volterra equations; LOTKA-VOLTERRA SYSTEMS; FOOD-CHAIN; DIFFERENTIAL-EQUATIONS; STRANGE ATTRACTORS; GLOBAL STABILITY; LIMIT-CYCLES; CHAOS; DYNAMICS; OMNIVORY; COMPETITION;

D O I：

10.1137/110825911

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The dynamics of the classic planar two-species Lotka-Volterra predator-prey model are well understood. We introduce a scavenger species that scavenges the predator and is also a predator of the common prey. For this model, we analytically prove that all trajectories are bounded in forward time, and numerically demonstrate persistent bounded paired cascades of period-doubling orbits over a wide range of parameter values. Standard analytical and numerical techniques are used in the analysis of this model, making it an ideal pedagogical tool. We include exercises and an open-ended project to promote mastery of these techniques.

引用

页码：523 / 546

页数：24

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