三类管理措施下的具有物质循环的渔业模型研究

发布时间：2018-05-29 13:41

本文选题：氮循环 + 渔业资源　；参考：《信阳师范学院》2017年硕士论文

【摘要】：渔业资源的可持续开发利用依赖水生动植物的存量和生产量,水生动植物的生存和生长不仅与水域生态环境有关,而且还与人们的开发能力有关,频繁的水华等水污染事件和人类的过度开发都是影响渔业资源可持续发展的重要因素.因此,本论文在建模型时既考虑了对水环境的生物治理措施,又考虑人们开发的目标收益,考虑到人们对渔业资源管理措施具有阶段性和脉冲性,本文基于一类具有营养物质循环的渔业模型,分别建立了变结构模型、微分代数模型和脉冲模型.本文分为4部分内容.第一部分,主要介绍了渔业资源、渔业生态系统的研究现状,水资源污染现状及治理方法.相关数学模型的定义及一些相关的预备知识.第二部分,主要考虑对藻类的阶段性收获,建立了一类变结构的渔业管理模型,包括连续收获模型和收获策略随资源存量变化的模型两部分.分别讨论其平衡态的存在性、稳定性及其分支情况,并且给出了变结构渔业模型的持久性证明.第三部分,考虑到经营管理者都要求有一定的的经济收益,建立了一类具有一定经济目标收益的微分代数渔业管理模型.利用Hurwitz判据、Jacobian矩阵等,讨论了系统平衡态的存在性及稳定性.利用Hopf分支定理讨论了经济平衡态的分支情况.第四部分,考虑到人类在治理水华过程中收获藻类和投放鱼类发生在不同时刻,建立了具有二次脉冲效应的脉冲模型.利用Floquet理论讨论了边界平衡点的存在性及其稳定性;进而给出持久性的相关讨论和相应的阈值.
[Abstract]:The sustainable development and utilization of fisheries resources depends on the stock and production of aquatic animals and plants, the survival and growth of which are related not only to the ecological environment of the waters, but also to the development capacity of people, Frequent water pollution events such as Shui Hua and human overexploitation are important factors that affect the sustainable development of fishery resources. Therefore, this paper not only considers the biological measures of water environment, but also takes into account the target income of people's development, considering the stage and pulse of fishery resources management measures. Based on a class of fishery models with nutrient cycling, a variable structure model, a differential algebraic model and a pulse model are established respectively. This paper is divided into four parts. The first part mainly introduces the research status of fishery resources, fishery ecosystem, water resources pollution and the treatment methods. The definition of relevant mathematical model and some related preparatory knowledge. In the second part, considering the periodic harvest of algae, a kind of fishery management model with variable structure is established, which includes two parts: continuous harvesting model and the model of harvesting strategy changing with resource stock. The existence, stability and bifurcation of the equilibrium state are discussed respectively, and the persistence proof of the variable-structure fishery model is given. In the third part a differential algebraic fisheries management model with certain economic objective income is established considering that managers and managers all require certain economic returns. By using Hurwitz criterion and Jacobian matrix, the existence and stability of equilibrium state of the system are discussed. The bifurcation of economic equilibrium state is discussed by using Hopf bifurcation theorem. In the fourth part, considering that algae harvesting and fish dropping occur at different times in the process of Shui Hua control, a pulse model with secondary pulse effect is established. The existence and stability of boundary equilibrium point are discussed by using Floquet theory, and the relevant discussion of persistence and the corresponding threshold are given.
【学位授予单位】：信阳师范学院
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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