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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics