Bifurcation delay - the case of the sequence: stable focus - unstable focus - unstable node

Eric Benoît (1)

1 MIA - Mathématiques, Image et Applications - EA 3165

Let us give a two dimensional family of real vector fields. We suppose that there exists a stationary point where the linearized vector field has successively a stable focus, an unstable focus and an unstable node. When the parameter moves slowly, a bifurcation delay appears due to the Hopf bifurcation. The studied question in this article is the continuation of the delay after the focus-node bifurcation.

Mots clés: Hopf-bifurcation; bifurcation-delay; slow-fast; canard; Airy; relief

Domaines: Systèmes dynamiques [math.DS]

Eric Benoît. Bifurcation delay - the case of the sequence: stable focus - unstable focus - unstable node. Discrete and Continuous Dynamical Systems - Series S, 2009, 2 (4), pp.911-929. ⟨hal-00354175⟩