title: Dynamic analysis of a fractional order delayed predator-prey system with harvesting.
abstract: In the study, we consider a fractional order delayed predator-prey system with harvesting terms. Our discussion is divided into two cases. Without harvesting, we investigate the stability of the model, as well as deriving some criteria by analyzing the associated characteristic equation. With harvesting, we investigate the dynamics of the system from the aspect of local stability and analyze the influence of harvesting to prey and predator. Finally, numerical simulations are presented to verify our theoretical results. In addition, using numerical simulations, we investigate the effects of fractional order and harvesting terms on dynamic behavior. Our numerical results show that fractional order can affect not only the stability of the system without harvesting terms, but also the switching times from stability to instability and to stability. The harvesting can convert the equilibrium point, the stability and the stability switching times.
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China.
authors.forename: Ping
authors.initials: P
authors.lastname: Song
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China. hyzhao1967@126.com.
authors.forename: Hongyong
authors.initials: H
authors.lastname: Zhao
authors.affiliation: Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China.|Department of Basic Course, Huaian College of Information Technology, Huaian, 223003, People's Republic of China.
authors.forename: Xuebing
authors.initials: X
authors.lastname: Zhang
mesh_terms: D000818:Animals; D003198:Computer Simulation; D003247:Conservation of Natural Resources; D004463:Ecology; D020387:Food Chain; D007313:Insecta; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics; D011235:Predatory Behavior; D013997:Time Factors
keywords: Fractional derivative; Harvesting; Predator–prey system; Stability; Time delay