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

• Autores: Joseph P. Previte, Kathleen A. Hoffman
• Localización: SIAM Review, ISSN 0036-1445, Vol. 55, Nº. 3, 2013, págs. 523-546
• Idioma: inglés
• DOI: 10.1137/110825911
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• Resumen

  • 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