Mansal Fulgence, Nguyen-Huu Tri, Auger Pierre, Balde Moussa
Département de mathématiques et informatique, Faculté des Sciences et techniques, UMI IRD 209, UMMISCO, IRD, Université Cheikh Anta Diop, Dakar, Senegal,
Acta Biotheor. 2014 Sep;62(3):305-23. doi: 10.1007/s10441-014-9227-7. Epub 2014 Jun 21.
We present a mathematical bioeconomic model of a fishery with a variable price. The model describes the time evolution of the resource, the fishing effort and the price which is assumed to vary with respect to supply and demand. The supply is the instantaneous catch while the demand function is assumed to be a monotone decreasing function of price. We show that a generic market price equation (MPE) can be derived and has to be solved to calculate non trivial equilibria of the model. This MPE can have 1, 2 or 3 equilibria. We perform the analysis of local and global stability of equilibria. The MPE is extended to two cases: an age-structured fish population and a fishery with storage of the resource.
我们提出了一个价格可变的渔业数学生物经济模型。该模型描述了资源、捕捞努力量以及假定随供需变化的价格的时间演变。供给是瞬时捕捞量，而需求函数假定为价格的单调递减函数。我们表明，可以推导出一个一般的市场价格方程（MPE），并且必须求解该方程才能计算模型的非平凡均衡。这个MPE可以有1个、2个或3个均衡。我们对均衡进行局部和全局稳定性分析。MPE被扩展到两种情况：年龄结构的鱼类种群和有资源存储的渔业。
