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December  2009, 2(4): 911-929. doi: 10.3934/dcdss.2009.2.911

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

Eric Benoît 1,

1. 

Université de La Rochelle, avenue Michel Crépeau, 17042 La Rochelle, France

Received  September 2008 Revised  June 2009 Published  September 2009

We consider 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. It is known that when the parameter moves slowly, a bifurcation delay appears due to the Hopf bifurcation. The main question investigated in this article is the continuation of the delay in the region of the unstable node. Another problem is to determine the input-output relation which characterizes all the possible delays.
Keywords: canard, bifurcation-delay, slow-fast, relief., Hopf-bifurcation, Airy.
Mathematics Subject Classification: Primary: 34E15, 34E18 ; Secondary: 34M6.
Citation: Eric Benoît. Bifurcation delay - the case of the sequence: Stable focus - unstable focus - unstable node. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : 911-929. doi: 10.3934/dcdss.2009.2.911
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