## Bulletin of the Belgian Mathematical Society - Simon Stevin

### Enhanced delay to bifurcation

#### 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

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

#### 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