Abstract for:Shedding Light on the Harvesting Control Rules in Abstract Bioeconomic Models
The theory of bifurcations and catastrophes is applied to the development of modifications of the Schaefer fishery model. The key variables are the stock of the bioresource, its natural net change, as well as the Man harvesting activity. The global and local analysis reveals quantitative and qualitative characteristics of open or closed loop control. Especially dangerous are the aggravation regimes arising from the dominance of the positive feedback connecting the biomass and the rate of its net change. The equations for excessive or sparing harvesting are derived. The time frames for collapses have been determined. This paper facilitates creation of more complex and realistic bioeconomic models and enhances Harvesting Control Rules.
Key words: renewable resource, depletion, maximum sustainable yield, harvesting control rule, aggravation mode, saddle-node bifurcation, catastrophe theory