Leard, Benjamin; Lewis, Catherine; Rebaza, Jorge Dynamics of ratio-dependent predator-prey models with nonconstant harvesting. (English) Zbl 1151.37062 Discrete Contin. Dyn. Syst., Ser. S 1, No. 2, 303-315 (2008). Summary: The dynamics of constant harvesting of a single species has been studied extensively within the framework of ratio-dependent predator-prey models. In this work, we investigate the properties of a Michaelis-Menten ratio-dependent predator-prey model with two nonconstant harvesting functions depending on the prey population. Equilibria and periodic orbits are computed and their stability properties are analyzed. Several bifurcations are detected as well as connecting orbits, with an emphasis on analyzing the equilibrium points at which the species coexist. Smooth numerical continuation is performed that allows computation of branches of solutions. Cited in 32 Documents MSC: 37N25 Dynamical systems in biology 92D25 Population dynamics (general) 34C60 Qualitative investigation and simulation of ordinary differential equation models 34D05 Asymptotic properties of solutions to ordinary differential equations 34C23 Bifurcation theory for ordinary differential equations 37C27 Periodic orbits of vector fields and flows Keywords:population dynamics; Michaelis-Menten ratio-dependent predator-prey model; equilibria and periodic orbits; bifurcations; stability properties PDFBibTeX XMLCite \textit{B. Leard} et al., Discrete Contin. Dyn. Syst., Ser. S 1, No. 2, 303--315 (2008; Zbl 1151.37062) Full Text: DOI