Optimal control for the nonlinear Fisher-Kolmogorov system with applications to aquatic plant management

Spatiotemporal dynamics of populations may be described by the reaction-diffusion Fisher-Kolmogorov model. In this work we have proposed a new formulation for a control problem of aquatic plants in a temporal dynamics. The solution of this problem is extended to a spatiotemporal Fisher-Kolmogorov system with multiple species of plants interacting in the same place. The control consists on human intervention as a strategy for management of the aquatic plants. In our applications, one plant and two plants cases have been considered. Simulation results are presented to show the effectiveness of the proposed control strategies.