Delayed stability switches in singularly perturbed predator–prey models

Abstract

In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V. F. Butuzov, N. N. Nefedov and K. R. Schneider, and an appropriate monotonicity assumption on the vector eld. The result is applied to identify all possible predator-prey models with quadratic vector elds allowing for the existence of canard solutions.