Dynamic analysis of wild and sterile mosquito release model with Poincaré map

In recent years, the application of impulsive semi-dynamic system in state-dependent feed-back control has attracted extensive attention, but most models only discuss their special cases without delving into their complex dynamics. Therefore, we establish the wild and sterile mosquito system with integrated mosquito control, and use the Poincaré map method to conduct a comprehensive analysis of the model dynamics. First, the main properties of Poincaré map such as monotonicity, continuous differentiability, extremum and fixed point are discussed. Second, we prove the existence and stability of boundary periodic solution and study the influence of its parameters on the system. Then the ex-istence and global stability of the order-1 periodic solution and the existence condition of the order-k (k > 1) periodic solution are analyzed. Finally, our conclusion is verified by numerical analysis. The results show that the population density of wild mosquitoes can be controlled below the threshold by integrated mosquito control.