双寡头的经济捕鱼策略

为了实现渔业资源的可持续利用 ,必须合理投入捕捞努力量 .在存在两个捕捞主体的情况下 ,分别就 Cournot模型和 Stackelberg模型分析了两个主体为了自身获得最大持续利润而投入的捕捞努力量 .与只有一个捕捞主体相比 ,当存在两个捕捞主体时 ,每个捕捞主体投入的捕捞努力量将增加或保持不变 ,但每个主体单位捕捞努力量所能取得的纯利润将减少 .产生这种低效率的原因在于每个主体只考虑自己投入的捕捞努力量对自己利润的影响 ,而不考虑对对方或社会产生的负面影响 .对渔业捕捞全面规划、综合管理是消除这种后果所必要的 .     

最优捕鱼模型

本文就渔场捕鱼策略问题建立了一个决策优化模型。该模型既考虑了鱼群变化的年内连续性,又考虑到年间离散性,在保证“持续捕捞”的前提条件下,使渔获量达到最大。 在分析过程中,我们拓宽了鱼群“死亡率’的含义。它包括“自然死亡率”和由于捕捞而引起的“死亡率”两个方面,我们把后者定义为“捕捞死亡牢”,这种处理方法给我们解决实际问题带来了极大的方便。 依据群体指数衰减规律,我们提出了实现可持续捕获的条件,得到一个比较稳定的捕捞强度系数,并通过计算机模拟验证。 模型的重要结论是:达到年收获量最高的捕捞强度系数F为17,收获量为3.87×10~8千克/年,渔业公司在5年内的最高总收获量为1.59×10~9千克。     

最佳捕鱼策略的数学模型

本文的数学模型提法清楚.相对于捕捞强度递增的不同予测值,对鱼群变化进行动态模拟,以求得到稳产,这不失为一种有启发性的处理方法。但由于未能对捕捞量—捕捞强度函数进行更为精确的解析或数值研究,结果未能达到最高产。     

最优捕鱼策略的设计

本问题是一个典型的可再生资源开发问题,因此我们以成熟的Scheafer模型为基础求解,在建模过程中,我们对各年龄组鱼在同一年中的数量变化规律应用微分方程进行分析,建立捕捞期和产卵期两个阶段各组鱼群的数量随时间变化的指数型方程。此后我们又对各组鱼群之间的数量关系建立按年份变化的离散型方程,最终获得即简单又比较精确的离散型迭代方程组。 在模型求解过程中,我们结合了计算机分析求解的技术,应用Mathematic软件以及WatcomC/C++编译器,通过编程序求出了问题的解,并以作图的方式给出了模型的直观表示,我们还在数学上对于鱼类分布结构的收敛性给予了严格的证明,从而得出如下结论; 可持续性捕捞的最优捕捞强度系数3龄鱼为7.2924/年,4龄鱼为17.3629/年,相应的年捕捞量为3.88×10~(11)克。 5年连续捕捞的最优捕捞强度系数3龄鱼为7.3836/年,4龄鱼为17.58/年,相应的年捕捞量为2.34401×10~(11)克,2.14852×10~(11)克,396176×10~(11)A?K#,3.77825×10~(11)克与3.82216×10~(11)克。 本模型具有较强的适用性和普遍性,建模过程中提出的对资源的开发和保护进行加权综合考虑的方法具有现实指导意义。     

持续高产捕鱼策略

本文基于鳀鱼产卵、孵化的突变性和死亡、被捕捞的连续性的假设,建立了鳀鱼生态系统的微分——差分模型。用数值模拟方法,分析了在各种捕捞强度下系统的稳定状态,并最终利用类似Leslie矩阵的方法检验了此时确为种群不变的稳定状态。在此基础上,对问题1),通过对[0,1]区间所有满足保持稳定状态捕捞强度系数p的搜索,得出使得年产量最高的最优值p=0.037,对应的年产量为6.44455万吨。对于问题2)分别讨论了5年中p不变和每年p发生变化的两种情况,用逐步求精的搜索法分别求解,得出两种情况下各自的最优策略,其产量分别为49.0575万吨和49.6284万吨。本文还进一步考虑了模型的改进,并讨论了以保证最大利润为目标的可持续捕捞策略,数值计算表明我们的模型是相当令人满意的。     

最优捕鱼策略模型

本文讨论了渔业资源开发项目中在实现可收获的前提下对某种鱼的最优捕捞策略。 针对问题一: 通过对4龄鱼在年末的两种不同状态(全部死亡;仍为4龄鱼)的考虑,得到了两个模型,再进一步考虑鱼的产卵和孵化是一个连续的过程,利用两个离散变量的几何平均来代替连续变量建立第三个模型,最后求解在计算机上实现。 针对问题二: 1.先假设每年捕捞强度相等,建立了一个简单模型; 2.再假设每年捕捞强度不相等,建立一个复杂模型; 3.最后给出鱼群生产能力破坏不太大的含义(即鱼群减少率的上限),在它的约束之下再建立一个模型。 本文最大的特点是:离散和连续相结合,在本文的后面又将各模型的结果进行了比较,并给出了理论上的解湿,得到令人满意的结果。     

巧妇难为无米之炊——由一道中考题想到的

在2003年大连中考数学试题中,有这样一道题目:某水产品养殖加工厂有200名工人,每名工人每天平均捕捞水产品50千克,或将当日所捕捞的水产品40千克进行精加工,已知每千克水产品直接出售可获利润6元,精加工后再出售,可获利润18元,设每天安排x名工人进行水产品精加工。     

太湖白鱼和梅鲚的数量增长模型

太湖的主要肉食性鱼类是白鱼,它是捕食梅鲚的主要鱼类.在建立了反映两者相互关系的数学模型后,分析了模型的稳定性、稳健性,通过数值模拟得到了种群数量随时间变化的曲线和相应的轨线,并探讨了捕捞强度、增殖放流对种群数量的影响.     

最优捕鱼策略

社会经济生活中,我们常遇到商业活动在一段时期内的最大收益问题,如森林管理等。这时,我们不仅要考虑商业活动的当前经济效益,还要考虑生态效益及由此产生的对整体经济效益的影响。 本文涉及的问题是渔业管理,即对一国定的渔场,在一段时间内,如何实现最大的收益,同时保证渔场能稳定生产,我们的基本思路是:考虑渔场生产过程中的两个相互制约的因素,年捕捞能力和再生产能力,从而确定最优管理策略。我们用微分方程来描述渔场鱼群数量随时间变化的规律,在此基础上确定整体效益为我们的目标函数,以渔场生产的稳定性要求为约束条件,分别对长期生产和固定期生产两种情况建立了规划模型。 在对长期生产模型的求解中,我们利用约束条件将目标函数化为一元函数,用计算机数值法确定近似的最优解,而在对固定期生产模型求解中,我们则构造一个整体效益函数,综合考虑年捕捞能力和年再生产能力,用计算机数值解法进行搜索逐年确定各年的最优策略,从而得出五年的总最优策略。 最后,我们对模型的稳定性进行敛定量的分析,并对模型进行了检验,确定模型较好地反映渔场最优捕鱼策略问题。     

有保护区的海洋渔业资源的临界稳定性分析

考虑一类渔业资源储量-捕捞力度模型,首先,本文运用中心流形定理确定系统的不动点在发生Flip分叉时的临界稳定性,然后,根据规范型理论确定系统的不动点在发生Neimark-Sacker分叉时的临界稳定性,最后,通过数值模拟验证了结论.     

变捕捞努力量收获模型控制

利用微分包含给出了努力量可变的收获模型,基于生存理论和求解线性规划给出了将单种群数量控制在某范围的方法.最后对于常用的Logistic模型,证明只要控制努力量就可以将种群数量控制在指定范围内.     

控藻鲢鱼的捕捞策略

鲢鱼是一种以水中浮游动植物为食的滤食性鱼类,利用鲢鱼控制蓝藻数量是一种有效的纯生物手段.分析蠡湖鲢鱼资源稳定的条件,建立鱼量的基本方程式及利润模型,给出利润与捕捞强度的关系和鱼群数量的变化趋势.最后得到了鲢鱼的放流与回捕策略.     

FEATURES OF BIOECONOMICS MODELS FOR THE OPTIMAL MANAGEMENT OF A FISHERY EXPLOITED BY TWO DIFFERENT FLEETS

ABSTRACT. After the extension of the Exclusive Economic Zone, in 1977, to 200 miles, most fish stocks came under jurisdiction of the adjacent coastal states. This development opened prospects of effective management of the open sea fisheries. Coastal states have the right to plan out the operation of so-called by Clarke and Munro “distant water fishing nations” from their Exclusive Economic Zone. Under some arrangements, a foreign fleet is allowed to harvest the resource in the Exclusive Economic Zone area. Clarke and Munro, in [1987] and [1991], focus on the issue of optimum terms and conditions of access and, in doing so, built a multiobjective model. The main goal of the present work is the development of a more general model including more variables and parameters related to the presence of a domestic fleet as well as a distant water fishing nation. The main difficulty resides in sharing the harvesting between the two fleets. The study responds to the realistic problemof coastal states who own enough resource stocks to allow harvesting by several kinds of fleets. Two optimal scenarios are developed, in each of them a solution is given.     

STANDARDIZATION OF CATCH-PER-UNIT-EFFORT FOR SHORT-TERM TRENDS IN CATCHABILITY

Examination of daily catch–per–unit–effort (CPUE) information on Pacific halibut revealed sharp declines that could not be explained by natural and fishing mortality. Catchability may have decreased during a fishing period because of local depletions of fish, changes in fish behavior, and other causes. Mathematical models of CPUE with a short–term catchability function of time or effort were based on a generalization of the DeLury method. A method of standardization was developed to account for the length of a fishing period and to correct for catchability. The effort model was best for Pacific halibut data and the application showed that standardization of CPUE is necessary to have a valid index of abundance when short–term changes in catchability occur.     

Maximum sustainable yield harvesting in an age‐structured fishery population model

A generic type age‐structured fishery population model consisting of two harvestable age classes is formulated. Optimal harvest rates are determined with uniform fishing mortality and perfectly selective fishing, respectively. Selectivity allows for differentiating the fishing mortality among different age classes. Sustainable yield–biomass functions are developed, and the maximum sustainable yield (MSY) solutions are found under both exploitation schemes. The gain of perfectly selective fishing over uniform (or biomass) fishing is examined under various assumptions, and it is proved that the benefit of selective harvesting increases when the harvestable fish population becomes more heterogeneous in terms of weights, or values. In contrast to the surplus production model, or Clark model, the analysis also demonstrates that MSY with different age classes is not purely a biological concept.     

A mixed integer programming model of a multicohort single-species fishery

Many marine fisheries are under pressure from overfishing. Fisheriesmanagement is a complex process because of the need to considerthe interaction of the biological components of the fishery,the technical characteristics of the fishing fleet, and theeconomic aspects of the fishing industry. In this paper, a mixedinteger programming (MIP) model for determining the policy tomaximize the long-run economic benefit from a single-speciesmulticohort fishery is developed. The model takes account ofthe biological, technical, and economic characteristics of thefishery, using integer variables to model the fishing activities.An iterative procedure for solving the model using commercialMIP software is described, and the viability of this procedureis illustrated using data for the western mackerel fishery.     

FISHING YIELD,CURVATURE AND SPATIAL BEHAVIOR: IMPLICATIONS FOR MODELING MARINE RESERVES

ABSTRACT. Given a paucity of empirical data, policymakers are forced to rely on modeling to assess potential impacts of creating marine reserves to manage fisheries. Many modeling studies of reserves conclude that fishing yield will increase (or decrease only modestly) after creating a reserve in a heavily exploited fishery. However, much of the marine reserves modeling ignores the spatial heterogeneity of fishing behavior. Contrary to empirical findings in fisheries science and economics, most models assume explicitly or implicitly that fishing effort is distributed uniformly over space. This paper demonstrates that by ignoring this heterogeneity, yield‐per‐recruit models systematically overstate the yield gains (or understate the losses) from creating a reserve in a heavily exploited fishery. Conversely, at very low levels of exploitation, models that ignore heterogeneous fishing effort overstate the fishing yield losses from creating a reserve. Starting with a standard yield‐per‐recruit model, the paper derives a yield surface that maps spatially differentiated fishing effort into total long‐run fishing yield. It is the curvature of this surface that accounts for why the spatial distribution of fishing effort so greatly affects predicted changes from forming a reserve. The results apply generally to any model in which the long‐run fishing yield has similar curvature to a two‐patch Beverton‐Holt model. A simulation of marine reserve formation in the California red sea urchin fishery with Beverton‐Holt recruitment, eleven patches, and common larval pool dispersal dynamics reinforces these results.     

Dynamics of a fishery system in a patchy environment with nonlinear harvesting

In this paper, a stock‐effort dynamical model with two fishing zones is discussed. The nonlinear harvesting function is assumed depending upon stock size as well as fishing effort. The migration of fish is considered between two zones. The harvesting vessels also move between zones to increase their revenue. The movements of fish and fishing vessels between zones are assumed to take place at a faster time scale as compared with processes involving growth and harvesting occurring at a slow time scale. The aggregated model is obtained for total fish stock and fishing effort. This aggregated (reduced) model is analyzed analytically as well as numerically. Biological and bionomic equilibria of the system are obtained, and criteria for local stability or instability of the system are derived. The impact of levels of taxation T on the fish population and on the revenue earned by the fishery is investigated. An optimal harvesting policy is also discussed using the Pontryagin's maximum principle. The aggregated model also exhibits Hopf and transcritical bifurcation with respect to the bifurcation parameter tax T. Numerical simulations are presented to illustrate the results.