Dynamics of a guanaco–sheep competitive system with unilateral and bilateral control

In this paper, based on a guanaco–sheep competitive system, we develop and analyze mathematical models with unilateral bilateral control for the management of overgrazing. We first dynamics uncontrolled system. It then follows analysis system impulsive by differential equation geometry theory. mainly prove existence stability order-1 periodic solution order-2 Some numerical simulations including bifurcation diagrams are carried out, which not only verify validity theoretical results, but also reveal some special dynamic phenomena, such as appearance higher-order solutions parameter intervals order change solution. Comparing strategy, encourage rather than sheep species.