Delayed stability switches in singularly perturbed predator-prey models

摘要

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 field. The result is applied to identify all possible predator prey models with quadratic vector fields allowing for the existence of canard solutions. (C) 2016 Elsevier Ltd. All rights reserved.