Bulletin of the Belgian Mathematical Society - Simon Stevin

Enhanced delay to bifurcation

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

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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

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

First available in Project Euclid: 5 December 2008

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Slow-fast systems Dynamical Bifurcations


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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