Can management measures ensure the biological and economical stabilizability of a fishing model?

The development of fishing management modeling was motivated by the need to understand mechanisms governing production flows of marine reserves. Several bioeconomic models were built and their analyses helped to identify management measures adapted to specific objectives. The approach adopted in this work must interest both fishermen (economics aspect: represented in the model by a price dynamics) and ecologist (stock durability: represented in the model by stock dynamics). First, we analyze the biological and economic stabilizability of a non-autonomous model involving a time-varying price and where the control is the catch rate. Then we introduce two management measures: the total allowable catch quota (TAC) measure during a fishing period, and the biological rest period. We study the alternating problem between these two measures. Finally, we evaluate the optimal time for each period according to biological and economic parameters.