Predator–prey systems with small predator's death rate
Copyright policy )Predator–prey systems with small predator's death rate
Summary: The goal of paper is to study canard relaxation oscillations of predator-prey systems with Holling type II of functional response when the death rate of the predator is very small and the conversion rate is uniformly positive. This paper is a natural continuation of \textit{C. Li} and \textit{H. Zhu} [J. Differ. Equations 254, No. 2, 879--910 (2013; Zbl 1257.34035)] and \textit{C. Li} [in: Mathematical sciences with multidisciplinary applications. In honor of Professor Christiane Rousseau, and in recognition of the Mathematics for Planet Earth initiative. Cham: Springer. 301--325 (2016; Zbl 1365.37064)] where both the death rate and the conversion rate are kept very small. We detect all limit periodic sets that can produce the canard relaxation oscillations after perturbations and study their cyclicity by using singular perturbation theory and a family blow-up.
slow-divergence integral, QA Mathematics / matematika, predator–prey systems; slow-divergence integral; slow–fast systems, Canard solutions to ordinary differential equations, slow-fast systems, Population dynamics (general), predator-prey systems, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, Singular perturbations for ordinary differential equations, Relaxation oscillations for ordinary differential equations, predator–prey systems, slow–fast systems, Mathematics
slow-divergence integral, QA Mathematics / matematika, predator–prey systems; slow-divergence integral; slow–fast systems, Canard solutions to ordinary differential equations, slow-fast systems, Population dynamics (general), predator-prey systems, Qualitative investigation and simulation of ordinary differential equation models, QA1-939, Singular perturbations for ordinary differential equations, Relaxation oscillations for ordinary differential equations, predator–prey systems, slow–fast systems, Mathematics
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