Articolo in rivista, 2020, ENG, 10.1007/978-3-030-41120-6_8

Optimal Control of Invasive Species with Budget Constraint: Qualitative Analysis and Numerical Approximation

Martiradonna A.; Diele F.; Marangi C.

Institute for Applied Mathematics (IAC) - CNR, Bari, Institute for Applied Mathematics (IAC) - CNR, Bari, Italy, , Italy

The containment of the invasive species is a widespread problem in the environmental management, with a significant economic impact. We analyze an optimal control model which aims to find the best temporal resource allocation strategy for the removal of an invasive species. We derive the optimality system in the state and control variables and we use the phase-space analysis to provide qualitative insights about the behavior of the optimal solution. Finally, for the state-costate variables which satisfy a boundary-valued nearly-Hamiltonian system, we propose exponential Lawson symplectic approximations applied in the forward-backward form. The numerical results related to an example of invasive plant considered in Baker, et al. (Nat Resour Model 31(4):e12190, 2018), confirm the qualitative findings provided by the state-control analysis.

SEMA SIMAI Springer Series 21 , pp. 147–164

Keywords

Invasive species, optimal control, dynamical systems, Boundary value Hamiltonian systems, Phase space analysis, Exponential Lawson Runge-Kutta

CNR authors

Diele Fasma, Marangi Carmela, Martiradonna Angela

CNR institutes

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