Predator–prey systems with small predator's death rate

Abstract

The goal of our paper is to study canard relaxation oscillations of predator-prey systems with Holling type II of functional response when the death rate of predator is very small and the conversion rate is uniformly positive. This paper is a natural continuation of [C. Li, H. Zhu, 2013; C. Li, 2016] where both the death rate and the conversion rate are kept very small. We detect all limit periodic sets that can produce the canard relaxation oscillations after perturbations and study their cyclicity by using singular perturbation theory and the family blow-up.