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

Dynamical Systems