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Mathematical modeling and control of population systems: applications in biological pest control. (English) Zbl 1139.92022
Summary: 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.
MSC:
92D30Epidemiology
49N90Applications of optimal control and differential games
37N35Dynamical systems in control
92D40Ecology
37N25Dynamical systems in biology
93A30Mathematical modelling of systems
34D20Stability of ODE
93B52Feedback control