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.