Articolo in rivista, 2019, ENG, 10.1016/j.nonrwa.2019.02.007

Optimal control of invasive species through a dynamical systems approach

Baker, Christopher M.; Diele, Fasma; Lacitignola, Deborah; Marangi, Carmela; Martiradonna, Angela

Univ Queensland; CSIRO Ecosyst Sci; CNR Bari; Univ Cassino & Lazio Meridionale

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we investigate problems where optimal control theory has been implemented. We show that transforming these problems from state-costate systems to state-control systems provides the complete qualitative description of the optimal solution and leads to its theoretical expression for free terminal time problems. We apply these techniques to two case studies: one of feral cats in Australia, where we use logistic growth; and the other of wild-boars in Italy, where we include an Allee effect. (C) 2019 The Authors. Published by Elsevier Ltd.

Nonlinear analysis: real world applications 49 , pp. 45–70

Keywords

Invasive species, Pontryagin's maximum principle, Optimal control, Dynamical systems, Boundary value Hamiltonian systems, Phase space analysis<bold>

CNR authors

Diele Fasma, Marangi Carmela, Martiradonna Angela

CNR institutes

IAC – Istituto per le applicazioni del calcolo "Mauro Picone"