Optimal control of invasive species through a dynamical systems approach

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 a...

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Bibliographic Details
Published in:Nonlinear analysis: real world applications 2019-10, Vol.49, p.45-70
Main Authors: Baker, Christopher M., Diele, Fasma, Lacitignola, Deborah, Marangi, Carmela, Martiradonna, Angela
Format: Article
Language:English
Subjects:
Boundary value Hamiltonian systems
Control theory
Dynamical systems
Environmental management
Invasive species
Nonnative species
Optimal control
Optimization
Phase space analysis
Pontryagin’s maximum principle
System effectiveness
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Summary: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.
ISSN:1468-1218
1878-5719
DOI:10.1016/j.nonrwa.2019.02.007