A dynamic analysis of a prey–predator population model with a nonlinear harvesting rate

PurposeIn this article, the author discusses dynamical behaviors of a prey-predator population model with nonlinear harvesting rate and offers a mathematical analysis of the model.Design/methodology/approachThe design is by using modelization of populations interaction, qualitative theory of ordinary différential equations, bifurcations analysis, invariant center manifolds theory and Dulac's criterion.FindingsThe author studies the stability of solutions and the existence of periodic solutions in the model, and proves the existence of some invariant sets and the production of a transcritical together with a saddle-node bifurcation.Practical implicationsThe author studies the effects of harvesting on the persistence and extinction properties and its influence in the perspectives of economic views.Originality/valueThe authors considers a predator–prey model with a new nonlinear form of harvesting rate. The author’s intention is to make conceptual adjustments to a well-known predator–prey model in order to incorporate the effects of harvesting.