Article citationsMore>>

De Maesschalck, P. and Schecter, S. (2016) The Entry-Exit Function and Geometric Singular Perturbation Theory. Journal of Differential Equations, 260, 6697-6715.
https://doi.org/10.1016/j.jde.2016.01.008

has been cited by the following article:

• TITLE: Relaxation Oscillations in a Slow-Fast Modified Rosenzweig-MacArthur Model

  AUTHORS: Jiao Wang, Youping Yang

  KEYWORDS: Rosenzweig-Macarthur Model, Slow-Fast Dynamics, Relaxation Oscillation, Geometric Singular Perturbation, Entry-Exit Function

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.13 No.4, April 24, 2025

  ABSTRACT: In this paper, the relaxation oscillation of a slow-fast Rosenzweig-MacArthur model is investigated. The existence of the relaxation oscillation cycle is obtained by means of geometric singular perturbation theory and entry-exit function. The asymptotical stability of the cycle which follows from the negativity of the Floquet multiplier further guarantees the uniqueness of the relaxation oscillation. The theoretical results are verified by numerical simulations.