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

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...

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Bibliographic Details
Published in:SIAM review 2013-01, Vol.55 (3), p.523-546
Main Authors: Previte, Joseph P., Hoffman, Kathleen A.
Format: Article
Language:English
Subjects:
EDUCATION
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Summary: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.
ISSN:0036-1445
1095-7200
DOI:10.1137/110825911