Dynamics analysis of a two-species competitive model with state-dependent impulsive effects

In this paper, we present two novel mathematical models of two-species competitive model with state-dependent impulsive control strategies, one is incorporating the density of one species as control threshold value, the other determines the control strategies by monitoring the densities of the two species. By the Poincaré map, analogue of Poincaré criterion and qualitative analysis method, some sufficient conditions on the existence and orbitally asymptotical stability of the semi-trivial periodic solution, positive order-1 or order-2 periodic solution of two models are presented. Furthermore, bifurcation diagrams and phase diagrams are investigated by means of numerical simulations, which illustrate the feasibility of our main results presented here.