Relaxation oscillations and canard explosion in a predator–prey system of Holling and Leslie types. (August 2017)

• Record Type: Journal Article
• Authors: Atabaigi, Ali; Barati, Ali
• Is Part Of: Nonlinear analysis. Volume 36(2017)
• Page Start: 139
• Page End: 153
• Publication Date: 2017-08
• Subjects: Relaxation oscillations -- Canard explosion -- Geometric singular perturbation theory -- Predator–prey system -- Holling and Leslie; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2017.01.006
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We give a geometric analysis of relaxation oscillations and canard cycles in a singularly perturbed predator–prey system of Holling and Leslie types. We discuss how the canard cycles are found near the Hopf bifurcation points. The transition from small Hopf-type cycles to large relaxation cycles is also discussed. Moreover, we outline one possibility for the global dynamics. Numerical simulations are also carried out to verify the theoretical results.