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

  • Renato HuzakEmail author


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.


Family blow-up Normal forms Singular perturbation theory Slow–fast Hopf point 



I would like to thank the referee for a number of useful comments.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Hasselt UniversityDiepenbeekBelgium

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