应用数学毕业论文-出海捕鱼模型比较.docVIP

出海捕鱼问题 The Problem of Fishing 届 系 专 业 学 号 学生姓名 指导教师 完成日期 年 月 日 摘 要 本文主要考虑出海捕鱼的最优问题，出海捕鱼追求的是最大产量或最优效益，为了使生态环境不受到破坏，同时实现捕鱼业的持续收获，首先要考虑鱼的自然增长率和捕捞率的关系，据此建立三种模型．一、产量模型，即追求鱼的最大产量，利用常微分方程解出稳定情况下渔场的鱼量及最大持续产量；二、效益模型：效益模型又分为不考虑银行利率等影响模型Ⅰ和考虑银行利率等影响模型Ⅱ；模型Ⅰ与产量模型相似，在控制捕捞强度下求出利润最大时的稳定鱼量及单位时间的持续产量，模型Ⅱ在模型Ⅰ的基础上引入折扣因子，从经济学上考虑长期效益，通过解欧拉方程求最优鱼量和持续捕捞量，最后在边际损失和边际得益平衡时得到最大效益。三、捕捞过度模型，通过比较单位捕捞费用、贷款实际利率和鱼的售价方面的关系分析资源枯竭的问题．最后通过比较上述模型得出最优模型． 关键词：鱼的自然增长率 捕鱼强度 捕捞系数 持续产量 最优效益 Abstract The paper main consideration the optimalization problem of goes to sea to catches fish, The pursue of go to sea catches fish is the greatest output or the most superior benefit, In order to cause the ecological environment do not be destructed, simultaneously realizes catching fish industry continues sustained yield, Must consider fishs natural increase rate and the fishing rate relations, according to the above explanation establishes three kind of models. First, the output model, the goal of this model is fishs greatest output, Using the differential equation solves the fishery fish quantity and the most great sustained production in the stable situation; The second model is benefit model: The benefit model divides into two；One do not consider the influence of bank rate —model I ，the other considers the influence of bank rate— model II; The model I is similar with the output model，with the control of fishing intensity they want to get the stable fish quantity and the sustained production, The model II introduces the discount factor at the base modelⅠ,It considers the long-term benefit from the economic, By the solution of Euler equation gets the most superior fish quantity and continous fishing quantity, Finally obtains the largest benefit when the boundary loss and the boundary achieves the balance. Third, over fishing model, Compared with the unit expense,the loan real interest rate and fishs selling price，then analysis the exhaustion of resources 。At the en