%0 Journal Article
%T Poincar¨¦ Map Approach to Global Dynamics of the Integrated Pest Management Prey-Predator Model
%A Cheng
%A Huidong
%A Li
%A Qingjian
%A Li
%A Weiming
%A Shi
%A Zhenzhen
%J -
%D 2020
%R https://doi.org/10.1155/2020/2376374
%X An integrated pest management prey-predator model with ratio-dependent and impulsive feedback control is investigated in this paper. Firstly, we determine the Poincar¨¦ map which is defined on the phase set and discuss its main properties including monotonicity, continuity, and discontinuity. Secondly, the existence and stability of the boundary order-one periodic solution are proved by the method of Poincar¨¦ map. According to the Poincar¨¦ map and related differential equation theory, the conditions of the existence and global stability of the order-one periodic solution are obtained when , and we prove the sufficient and necessary conditions for the global asymptotic stability of the order-one periodic solution when . Furthermore, we prove the existence of the order-k periodic solution under certain conditions. Finally, we verify the main results by numerical simulation
%U https://www.hindawi.com/journals/complexity/2020/2376374/