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

TL;DR

This paper develops optimal control strategies for managing aquatic plant populations modeled by a spatiotemporal Fisher-Kolmogorov system, demonstrating effectiveness through simulations for single and multiple species scenarios.

Contribution

It introduces a novel control formulation for the Fisher-Kolmogorov model applied to aquatic plant management, extending to multi-species interactions.

Findings

Control strategies effectively reduce plant populations in simulations.

The approach handles both single and multiple species cases.

Simulation results validate the proposed control methods.

Abstract

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.