Bulletin of the Belgian Mathematical Society - Simon Stevin

Enhanced delay to bifurcation

Jean--Pierre Françoise, Claude Piquet, and Alexandre Vidal

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Abstract

We present an example of slow-fast system which displays a full open set of initial data so that the corresponding orbit has the property that given any $\epsilon$ and $T$, it remains to a distance less than $\epsilon$ from a repulsive part of the fast dynamics and for a time larger than $T$. This example shows that the common representation of generic fast-slow systems where general orbits are pieces of slow motions near the attractive parts of the critical manifold intertwined by fast motions is false. Such a description is indeed based on the condition that the singularities of the critical set are folds. In our example, these singularities are transcritical.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 5 (2008), 825-831.

Dates
First available in Project Euclid: 5 December 2008

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1228486410

Digital Object Identifier
doi:10.36045/bbms/1228486410

Mathematical Reviews number (MathSciNet)
MR2484135

Zentralblatt MATH identifier
1195.34082

Subjects
Primary: 34C29: Averaging method 34C25: Periodic solutions 58F22

Keywords
Slow-fast systems Dynamical Bifurcations

Citation

Françoise, Jean--Pierre; Piquet, Claude; Vidal, Alexandre. Enhanced delay to bifurcation. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 5, 825--831. doi:10.36045/bbms/1228486410. https://projecteuclid.org/euclid.bbms/1228486410


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