Optimal control of invasive species through a dynamical systems approach. (October 2019)

• Record Type: Journal Article
• Authors: Baker, Christopher M.; Diele, Fasma; Lacitignola, Deborah; Marangi, Carmela; Martiradonna, Angela
• Is Part Of: Nonlinear analysis. Volume 49(2019)
• Page Start: 45
• Page End: 70
• Publication Date: 2019-10
• Subjects: Invasive species -- Pontryagin's maximum principle -- Optimal control -- Dynamical systems -- Boundary value Hamiltonian systems -- Phase space analysis; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.02.007
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.