Mathematical modeling and control of population systems: Applications in biological pest control

被引：62

作者：

Rafikov, M. ^{[1
]}

Balthazar, J. M. ^{[2
]}

von Bremen, H. F. ^{[3
]}

机构：

[1] Ijui Univ, UNJUI, Dept Phys Stat & Math, BR-98700000 Ijui, RS, Brazil

[2] Univ Estadual Paulista, Dept Stat Appl Math & Computat, BR-13500230 Rio Claro, SP, Brazil

[3] Calif State Polytech Univ Pomona, Dept Math & Stat, Pomona, CA 91768 USA

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2008年 / 200卷 / 02期

关键词：

mathematical modeling; biological pest control; linear feedback control; Kolmogorov system; Lotka Volterra system;

D O I：

10.1016/j.amc.2007.11.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to apply methods from optimal control theory, and from the theory of dynamic systems to the mathematical modeling of biological pest control. The linear feedback control problem for nonlinear systems has been formulated in order to obtain the optimal pest control strategy only through the introduction of natural enemies. Asymptotic stability of the closed-loop nonlinear Kolmogorov system is guaranteed by means of a Lyapunov function which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation, thus guaranteeing both stability and optimality. Numerical simulations for three possible scenarios of biological pest control based on the Lotka-Volterra models are provided to show the effectiveness of this method. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：557 / 573

页数：17