A viability analysis for a bio-economic model

This paper presents a simple dynamic model dealing with the management of a marine renewable resource. But instead of studying the ecological and econ omic interactions in terms of equilibrium or optimal control, we pay much a ttention to the viability of the system or, in a symmetric way, to crisis s ituations. These viability/crisis situations are defined by a set of econom ic and biological state constraints. The analytical study focuses on the co mpatibility between the state constraints and the controlled dynamics. Usin g the mathematical concept of viability kernel, we reveal the situations an d, if possible, management options to guarantee a perennial system. Going f urther, we define 'overexploitation' indicators by the time of crisis funct ion. In particular, we point out irreversible overexploitation configuratio ns related to the resource extinction. (C) 2001 Elsevier Science B.V. All r ights reserved.