Banasiak, JacekSeuneu Tchamga, M.S.Szymańska-Dȩbowska, Katarzyna2018-11-232019-03Banasiak, 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. 776-795.0022-247X (print)1096-0813 (online)10.1016/j.jmaa.2018.11.013http://hdl.handle.net/2263/67305In 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.en© 2018 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications, vol. 471, no. 1-2, pp. 776-795, 2019. doi : 10.1016/j.jmaa.2018.11.013.Backward bifurcationCanard solutionsDelayed stability switchMultiple time scalesPredator–prey modelsSingularly perturbed dynamical systemsPostprint Article