Food chain chaos due to Shilnikov’s orbit
- 1 September 2002
- journal article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 12 (3) , 533-538
- https://doi.org/10.1063/1.1482255
Abstract
Assume that the reproduction rate ratio zeta of the predator over the prey is sufficiently small in a basic tri-trophic food chain model. This assumption translates the model into a singularly perturbed system of two time scales. It is demonstrated, as a sequel to the earlier paper of Deng [Chaos 11, 514-525 (2001)], that at the singular limit zeta=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio epsilon of the top-predator over the predator is greater than a modest value epsilon(0). The additional conditions under which such a singular orbit may occur are also explicitly given. (c) 2002 American Institute of Physics.Keywords
This publication has 28 references indexed in Scilit:
- Chaotic dynamics of a microbial system of coupled food chainsEcological Modelling, 2001
- On Šilnikov′s Homoclinic-Saddle-Focus TheoremJournal of Differential Equations, 1993
- Slow-fast limit cycles in predator-prey modelsEcological Modelling, 1992
- Singular perturbation of relaxed periodic orbitsJournal of Differential Equations, 1987
- Persistent unstable equilibria and closed orbits of a singularly perturbed equationJournal of Differential Equations, 1985
- Stretching and Folding in Lynx Fur Returns: Evidence for a Strange Attractor in Nature?The American Naturalist, 1984
- Ecological Scaling: Mammals and BirdsAnnual Review of Ecology and Systematics, 1983
- An allometric approach to population cycles of mammalsJournal of Theoretical Biology, 1983
- Spiral Chaos in a Predator-Prey ModelThe American Naturalist, 1979
- Quantitative universality for a class of nonlinear transformationsJournal of Statistical Physics, 1978