【作者】 赵晨；

【导师】 宋新宇；

【作者基本信息】 信阳师范学院 ， 基础数学， 2019， 硕士

【摘要】 水产业的可持续发展不仅依赖水产养殖和捕捞技术,更依托于水域生态系统的环境,水体质量健康与否是影响水产业良性发展的关键因素.在水环境中,营养物质缺乏或过量,会使得健康水体呈现贫营养或富营养状态.水体的贫、富营养化都将极大阻碍水产业的发展,因此需采用人工管理措施来改善水质.本文基于水产业管理问题,引入变消耗这一概念,利用常微分方程、脉冲微分方程来研究营养物质与浮游生物间的相互作用,并研究相关数学问题.第一章,介绍了水产业、水环境现状以及针对不同水体的人工管理措施,并介绍相关生物数学模型的研究现状和一些预备知识.第二章,将浮游生物对营养物质的消耗率视为关于营养浓度的函数,建立一类具有变消耗率的营养-浮游生物模型.分析连续系统解的正性与有界性,讨论正平衡态的存在性和稳定性.通过讨论极限环的存在性,表明在一定条件下,浮游生物数量呈周期性变化.第三章,基于水产养殖的实际以及对贫营养水体的管理措施,在第二章模型的基础上,考虑周期投放营养物质对水体的影响,建立一类具有周期投放营养的浮游生物模型,并研究浮游植物灭绝的周期解的存在性和全局稳定性的条件.第四章,针对富营养水体中混凝沉降除藻的思想,在第二章模型的基础上,考虑对浮游植物的状态反馈控制问题,建立具有状态脉冲控制的营养-浮游生物模型.利用后继函数和Poincaré映射讨论了模型阶1周期解的存在性和稳定性.更多还原

【Abstract】 Sustainable development of aquaculture depends not only on aquaculture and fishing technology,but also on the environment of aquatic ecosystem.The health of water quality is the key factor affeeting the healthy development of aquaculture.In water environment,lack or excess of nutrients can lead to poor nutrition or eutrophication in healthy water body.Poverty and eutrophication of water body will greatly hinder the development of aquatic industry.Artificial management measures are needed to improve water quality.Based on the problem of aquaculture management,the concept of variable consumption is introduced in this paper.The interaction between nutrition and plankton is investigated by using impulse differential equation and ordinary differential equation,and the related mathematical problems is studied.The first chapter introduces the present situation of aquaculture,water environment and the artificial management measures for different water bodies.The research status of relevant biomathematical models and some preliminary knowledge are also introduced.In the second chapter,the nutrient consumption rate of plankton is regarded as a function of nutrient concentration,and a nutrient-plankton model with variable consumption rate is established.The positive and boundedness of solutions for continuous system are analyzed,the existence and stability of positive equilibrium are discussed.By discussing the existence of limit cycles,it is shown that the number of plankton varies periodically under certain conditions.In the third chapter,based on the aquaculture situation and the management measures of poor nutrient water,considering the effect of periodic nutrient input on water body on the basis of chapter 2 model,a kind of plankton model with periodic nutrient input is established.The conditions for the existence and global stability of periodic solution to phytoplankton extinction are studied.In the fourth chapter,aiming at the idea of algae removal by coagulation sedimentation in eutrophic water,a nutrient-phytoplankton model with state pulse control is established on the basis of chapter 2 model,considering the state feedback control of phytoplankton.The existence and stability of order-1 periodic solution are discussed by means of successor fuction and Poincaré map.更多还原