AN APPLICATION OF THE SEPARATION PRINCIPLE FOR DETECTING SLOW-FAST LIMIT-CYCLES IN A 3-DIMENSIONAL SYSTEM

A geometric method (called the separation principle) is used in this paper for detecting limit cycles in a slow-fast dynamical system describing a food chain with trophic levels with diversified time responses. The analysis is very simple and based on singular-perturbation arguments. The limit cycle resulting from the method is composed of a concatenation of catastrophic transitions occurring at different speeds.