A viability analysis for a bio-economic model

Abstract

This paper presents a simple dynamic model dealing with the management of a marine renewable resource. But instead of studying the ecological and economic interactions in terms of equilibrium or optimal control, we pay much attention to the viability of the system or, in a symmetric way, to crisis situations. These viability/crisis situations are defined by a set of economic and biological state constraints. The analytical study focuses on the compatibility between the state constraints and the controlled dynamics. Using the mathematical concept of viability kernel, we reveal the situations and, if possible, management options to guarantee a perennial system. Going further, we define ‘overexploitation’ indicators by the time of crisis function. In particular, we point out irreversible overexploitation configurations related to the resource extinction.