Entry–Exit Functions in Fast–Slow Systems with Intersecting Eigenvalues

Panagiotis Kaklamanos, Christian Kuehn, Nikola Popović, Mattia Sensi

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study delayed loss of stability in a class of fast–slow systems with two fast variables and one slow one, where the linearisation of the fast vector field along a one-dimensional critical manifold has two real eigenvalues which intersect before the accumulated contraction and expansion are balanced along any individual eigendirection. That interplay between eigenvalues and eigendirections renders the use of known entry–exit relations unsuitable for calculating the point at which trajectories exit neighbourhoods of the given manifold. We illustrate the various qualitative scenarios that are possible in the class of systems considered here, and we propose novel formulae for the entry–exit functions that underlie the phenomenon of delayed loss of stability therein.

Original languageEnglish
JournalJournal of Dynamics and Differential Equations
DOIs
StateAccepted/In press - 2023
Externally publishedYes

Keywords

  • Delayed loss of stability
  • Entry–exit function
  • Fast–slow systems
  • Geometric singular perturbation theory
  • Ordinary differential equations
  • Transcritical bifurcation

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