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- Mathematical modeling and control of population systems: Applications in biological pest control
- University Ijuí
- Universidade Estadual Paulista (UNESP)
- California State Polytechnic University, Pomona
- 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 B.V. All rights reserved.
- Applied Mathematics and Computation. New York: Elsevier B.V., v. 200, n. 2, p. 557-573, 2008.
- Elsevier B.V.
- mathematical modeling
- biological pest control
- linear feedback control
- Kolmogorov system
- Lotka Volterra system
- Acesso restrito
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