title: Z-type control of populations for Lotka-Volterra model with exponential convergence.
abstract: The population control of the Lotka-Volterra model is one of the most important and widely investigated issues in mathematical ecology. In this study, assuming that birth rate is controllable and using the Z-type dynamic method, we develop Z-type control laws to drive the prey population and/or predator population to a desired state to keep species away from extinction and to improve ecosystem stability. A direct controller group is initially designed to control the prey and predator populations simultaneously. Two indirect controllers are then proposed for prey population control and predator population control by exerting exogenous measure on another species. All three control laws possess exponential convergence performances. Finally, the corresponding numerical simulations are performed. Results substantiate the theoretical analysis and effectiveness of such Z-type control laws for the population control of the Lotka-Volterra model.
authors.affiliation: School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China. Electronic address: zhynong@mail.sysu.edu.cn.
authors.forename: Yunong
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China.
authors.forename: Xiaogang
authors.initials: X
authors.lastname: Yan
authors.affiliation: School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China; College of Information Science and Engineering, Jishou University, Jishou 416000, China.
authors.forename: Bolin
authors.initials: B
authors.lastname: Liao
authors.affiliation: School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China.
authors.forename: Yinyan
authors.initials: Y
authors.lastname: Zhang
authors.affiliation: School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China; SYSU-CMU Shunde International Joint Research Institute, Foshan 528300, China; Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangzhou 510640, China.
authors.forename: Yaqiong
authors.initials: Y
authors.lastname: Ding
mesh_terms: D000818:Animals; D020387:Food Chain; D008962:Models, Theoretical; D011155:Population Control
keywords: Exponential convergence; Lotka–Volterra model; Numerical simulation; Population control; Z-type controller