Enhanced delay to Bifurcation

TL;DR

This paper presents a fast-slow dynamical system where most trajectories stay near an unstable manifold for extended periods, illustrating complex delay phenomena in bifurcation scenarios.

Contribution

It introduces a specific example of a fast-slow system exhibiting prolonged delay near an unstable manifold, highlighting new dynamical behaviors.

Findings

Most orbits remain close to the unstable manifold for long durations

Demonstrates delay phenomena in bifurcation scenarios

Provides a concrete example of complex dynamical behavior

Abstract

This article provides an example of fast-slow system such that most orbits remain as close as possible to the unstable manifold of the fast dynamics for an arbitrarily long time.