Spatio-temporal population control applied to management of aquatic plants

• Published in: Ecological modelling 2019-04, Vol.398, p.77-84
• Main Authors: Frighetto, Daiane Frighetto, Souza, Gustavo Maia, Molter, Alexandre
• Format: Article
• Language: English
• Subjects: Control; Fisher–Kolmogorov equation; Fourier transform; Management of aquatic plants
• ISSN: 0304-3800; 1872-7026
• DOI: 10.1016/j.ecolmodel.2018.09.027

•Optimal control strategy applied to a biological system.•Control of a spatio-temporal biological system, consisting of aquatic plants.•Solution to the spatio-temporal model with control obtained through the finite Fourier transform. Reaction-diffusion models can be used to describe temporal and spatial dynamics of populations. When the interests is the relationship of a given species with the environment in which it is inserted, we can model this phenomenon through the equation of Fisher–Kolmogorov that, in a mathematical sense, consider the existence of a source term, that represents both the reproduction and the growth rate of a population up to the medium's carrying capacity. Through this equation it is possible to describe the behaviour of some animals, plants, bacteria and cells, for example, in order to predict the growth and invasion of these population, and control them if necessary. Thus, in this work we propose to introduce a control strategy in a biological system consisting of aquatic plants, in which the configuration is the same as the control function introduced in a logistic model. The solution to the reaction-diffusion model with control is obtained through the finite Fourier transform. This strategy, in practical terms, is based on the withdrawal of plants by human management. Computational simulations will be presented to illustrate the efficiency of the control strategy adopted.