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