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

Eric Benoît

doi:10.3934/dcdss.2009.2.911

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2009, Volume 2, Issue 4: 911-929. Doi: 10.3934/dcdss.2009.2.911

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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

Received: August 31, 2008

Revised: May 31, 2009

Published: November 2009

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Abstract

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.

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Mathematics Subject Classification: Primary: 34E15, 34E18 ; Secondary: 34M60.

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