Cyclicity of the limit periodic sets for a singularly perturbed Leslie-Gower predator-prey model with prey harvesting (Q6567211)

The authors study a Leslie-Gower predator-prey model with Michaelis-Men\-ten-type harvesting [\textit{R.P.~Gupta}, \textit{M.~Banerjee}, and \textit{P.~Chandra}, Differ. Equ. Dyn. Syst. 20, 339--366 (2012)] under the assumption that the intrinsic growth rate of predator is much lower than that of prey. Their focus is on the cyclicity of various limit periodic sets that include generic contact points, slow-fast canard cycles, double canard phenomena, and transitory canards, among others. In particular, they determine the maximum number and stability properties of limit cycles generated by slow-fast cycles that contain generic or degenerate canard points; furthermore, they prove the occurrence of stable relaxation oscillation in the model. Their approach is based on geometric singular perturbation theory [\textit{N. Fenichel}, J. Differ. Equations 31, 53--98 (1979; Zbl 0476.34034)] and the blow-up technique [\textit{F.~Dumortier} and \textit{R.~Roussarie}, Canard cycles and center manifolds. Mem. Am. Math. Soc. 577 (1996; Zbl 0851.34057)] in general, and on the notions of a (modified) slow divergence integral and the entry-exit function in particular; additionally, they perform a less standard construction that relies on (generalised) normal sectors [\textit{Y.~Tang} and \textit{W.~Zhang}, Nonlinearity 17(4), 1407--1426 (2004; Zbl 1089.34028)]. Finally, the authors illustrate their findings numerically in the scenarios where relaxation oscillation or canard explosion [\textit{M.~Krupa} and \textit{P.~Szmolyan}, J. Differ. Equations 174(2), 312--368 (2001; Zbl 0994.34032)] are observed, and they provide ecological interpretation.