Canard Explosion Near Non-Liénard Type Slow–Fast Hopf Point

Abstract

In this paper we study birth of canards near a smooth slow–fast Hopf point of non-Liénard center type which plays an important role in slow–fast codimension 3 saddle and elliptic bifurcations. We show that the number of limit cycles created in the birth of canards in such a slow–fast non-Liénard case is finite. Our paper is also a natural continuation of Dumortier and Roussarie (Discrete Contin Dyn Syst Ser S 2(4):723–781, 2009) where slow–fast Hopf points of Liénard type have been studied. We use geometric singular perturbation theory and the family blow-up.