Relaxation oscillations and canard explosion in a predator-prey system of Holling and Leslie types

We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator prey system of Honing and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results. (C) 2017 Elsevier Ltd. All rights reserved.