Abstract
Assume that the reproduction rate ratio ζ 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 ζ=0, a singular Shilnikov's saddle-focus homoclinic orbit can exist as the reproduction rate ratio e of the top-predator over the predator is greater than a modest value ε0. The additional conditions under which such a singular orbit may occur are also explicitly given.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 533-538 |
| Number of pages | 6 |
| Journal | Chaos |
| Volume | 12 |
| Issue number | 3 |
| DOIs | |
| State | Published - Sep 2002 |
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
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Cite this
Deng, B., & Hines, G. (2002). Food chain chaos due to Shilnikov's orbit. Chaos, 12(3), 533-538. https://doi.org/10.1063/1.1482255