Consideration is given to a basic food chain model satisfying the trophic time diversification hypothesis which translates the model into a singularly perturbed system of three time scales. It is demonstrated that in some realistic system parameter region, the model has a unimodal or logistic-like Poincaré return map when the singular parameter for the fastest variable is at the limiting value 0. It is also demonstrated that the unimodal map goes through a sequence of period-doubling bifurcations to chaos. The mechanism for the creation of the unimodal criticality is due to the existence of a junction-fold point [B. Deng, J. Math. Biol. 38, 21-78 (1999)]. The fact that junction-fold points are structurally stable and the limiting structures persist gives us a rigorous but dynamical explanation as to why basic food chain dynamics can be chaotic.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics