TITLE:
Canard Solutions in a Predator-Prey Model
AUTHORS:
Guojian Lin
KEYWORDS:
Canard Explosion, Relaxation Oscillation, Predator-Prey Model, Geometric Singular Perturbation Theory
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.5,
May
27,
2022
ABSTRACT: The canard explosion phenomenon in a predator-prey model with Michaelis-Menten functional response is analyzed in this paper by employing the geometric singular perturbation theory. First, some turning points, such as, fold point, transcritical point, pitchfork point, canard point, are identified; then Hopf bifurcation, relaxation oscillation, together with the canard transition from Hopf bifurcation to relaxation oscillation are discussed.