Viability Kernel for Ecosystem Management Models

TL;DR

This paper analyzes the viability kernel in ecosystem management models, providing explicit descriptions under certain conditions and illustrating its application with a case study on Peruvian marine ecosystems.

Contribution

It offers a new explicit characterization of the viability kernel for nonlinear ecosystem models with constraints, aiding sustainable management strategies.

Findings

Explicit viability kernel description under boundary growth conditions

Application to Peruvian hake-anchovy ecosystem model

Numerical illustration demonstrating practical relevance

Abstract

We consider sustainable management issues formulated within the framework of control theory. The problem is one of controlling a discrete--time dynamical system (e.g. population model) in the presence of state and control constraints, representing conflicting economic and ecological issues for instance. The viability kernel is known to play a basic role for the analysis of such problems and the design of viable control feedbacks, but its computation is not an easy task in general. We study the viability of nonlinear generic ecosystem models under preservation and production constraints. Under simple conditions on the growth rates at the boundary constraints, we provide an explicit description of the viability kernel. A numerical illustration is given for the hake--anchovy couple in the Peruvian upwelling ecosystem.