Dynamics of ratio-dependent Predator-Prey models with nonconstant harvesting

The dynamics of constant harvesting of a single species has been studied extensivelywithin the framework of ratio-dependent predator-prey models. In this work, weinvestigate the properties of a Michaelis-Menten ratio-dependent predator-prey modelwith 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 onanalyzing the equilibrium points at which the species coexist. Smooth numericalcontinuation is performed that allows computation of branches of solutions.