Canard solutions in equations with backward bifurcations of the quasi-steady state manifold

In this paper we consider a delayed exchange of stability for solutions of a singularly perturbed nonautonomous equation in the case when a backward bifurcation of its quasi-steady (critical) manifolds occurs. This result is applied to provide a precise description of canard solutions to singularly perturbed predator–prey models of Rosenzweig–MacArthur and Leslie–Gowers type.