Canard solutions in equations with backward bifurcations of the quasi-steady state manifold

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Authors

Banasiak, Jacek
Seuneu Tchamga, M.S.
Szymańska-Dȩbowska, Katarzyna

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Elsevier

Abstract

In this paper we consider a delayed exchange of stability for solutions of a singularly perturbed nonautonomous equation in the case when a backward bifurcation of its quasi-steady (critical) manifolds occurs. This result is applied to provide a precise description of canard solutions to singularly perturbed predator–prey models of Rosenzweig–MacArthur and Leslie–Gowers type.

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Keywords

Backward bifurcation, Canard solutions, Delayed stability switch, Multiple time scales, Predator–prey models, Singularly perturbed dynamical systems

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Citation

Banasiak, J., Seuneu Tchamga, M.S. & Szymańska-Dȩbowska, K. 2019, 'Canard solutions in equations with backward bifurcations of the quasi-steady state manifold', Journal of Mathematical Analysis and Applications, vol. 471, no. 1–2, pp. 776-795.