Rafikov, M.Balthazar, José Manoel [UNESP]von Bremen, H. F.2013-09-302014-05-202013-09-302014-05-202008-07-01Applied Mathematics and Computation. New York: Elsevier B.V., v. 200, n. 2, p. 557-573, 2008.0096-3003http://hdl.handle.net/11449/24897The 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 B.V. All rights reserved.557-573engmathematical modelingbiological pest controllinear feedback controlKolmogorov systemLotka Volterra systemArtigo10.1016/j.amc.2007.11.036WOS:000256441700009Acesso restrito