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.
The objective of the current paper is to investigate the dynamics of a new predator–prey model, where the prey species obeys the law of logistic growth and is subjected to a non-smooth switched harvest: when the density of the prey is below a switched value, the harvest has a linear rate. Otherwise, the harvesting rate is constant. The equilibria of the proposed system are described, and the boundedness of its solutions is examined. We discuss the existence of periodic solutions; we show the appearance of two limit cycles, an unstable inner limit cycle and a stable outer one. As the values of the model parameters vary, several kinds of bifurcation for the model are detected, such as transcritical, saddle–node, and Hopf bifurcations. Finally, some numerical examples of the model are performed to confirm the theoretical results obtained.
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