Delayed stability switches in singularly perturbed predator–prey models. (June 2017)

• Record Type: Journal Article
• Authors: Banasiak, J.; Tchamga, M.S. Seuneu
• Is Part Of: Nonlinear analysis. Volume 35(2017)
• Page Start: 312
• Page End: 335
• Publication Date: 2017-06
• Subjects: Singularly perturbed dynamical systems -- Multiple time scales -- Tikhonov theorem -- Delayed stability switch -- Predator–prey models -- Canard solutions; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.10.013
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: In this paper we provide an elementary proof of the existence of canard solutions for a class of singularly perturbed planar systems in which there occurs a transcritical bifurcation of the quasi steady states. The proof uses the one-dimensional result proved by V.F. Butuzov, N.N. Nefedov and K.R. Schneider, and an appropriate monotonicity assumption on the vector field. The result is applied to identify all possible predator–prey models with quadratic vector fields allowing for the existence of canard solutions.