title: Theoretical study and control optimization of an integrated pest management predator-prey model with power growth rate.
abstract: This work presents a pest control predator-prey model, where rate of change in prey density follows a scaling law with exponent less than one and the control is by an integrated management strategy. The aim is to investigate the change in system dynamics and determine a pest control level with minimum control price. First, the dynamics of the proposed model without control is investigated by taking the exponent as an index parameter. And then, to determine the frequency of spraying chemical pesticide and yield releases of the predator, the existence of the order-1 periodic orbit of the control system is discussed in cases. Furthermore, to ensure a certain robustness of the adopted control, i.e., for an inaccurately detected species density or a deviation, the control system could be stabilized at the order-1 periodic orbit, the stability of the order-1 periodic orbit is verified by an stability criterion for a general semi-continuous dynamical system. In addition, to minimize the total cost input in pest control, an optimization problem is formulated and the optimum pest control level is obtained. At last, the numerical simulations with a specific model are carried out to complement the theoretical results.
authors.affiliation: School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China.
authors.forename: Kaibiao
authors.initials: K
authors.lastname: Sun
authors.affiliation: Department of Mathematics, Swinburne University of Technology, Hawthorn VIC 3122, Australia.
authors.forename: Tonghua
authors.initials: T
authors.lastname: Zhang
authors.affiliation: School of Information Engineering, Dalian University, Dalian 116622, China. Electronic address: tianyuan1981@163.com.
authors.forename: Yuan
authors.initials: Y
authors.lastname: Tian
mesh_terms: D000818:Animals; D018533:Biomass; D020387:Food Chain; D008962:Models, Theoretical; D010571:Pest Control
keywords: Integrated pest management; Optimization; Order-1 periodic orbit; Predator–prey system; Stability