具有外来物种入侵的生物系统的分析与控制

发布时间:2018-03-10 12:25

  本文选题:外来物种入侵 切入点:生物经济系统 出处:《沈阳工业大学》2017年硕士论文 论文类型:学位论文


【摘要】:生物数学是应用数学思维,尝试从数学的角度研究和解决生物学上的问题,外来物种入侵常常损害本地的生态系统和地理构造,给生产生活造成了不良影响。用生物数学来研究外来物种入侵下的生态系统,了解经济生产和种群的动态学行为,对人类社会的稳定和发展能起到一定的积极作用。本文以外来物种入侵为背景,介绍了三种不同生物关系下的生态系统,包括捕食关系、抑制关系和竞争关系,三种生态系统都考虑了种群分阶段结构的情况。首先,根据外来物种与原生态系统中的物种存在的捕食关系,对分阶段结构的带功能反应函数的生态系统做永久性分析;其次,根据广义生物经济理论和考虑入侵的物种释放化学物质影响本地物种且本地物种出现时滞变化的情况,进行了分阶段结构的时滞生物模型的Hopf分岔、平衡点周期性分析;最后,考虑外来物种与本地物种存在竞争关系,进行了加入特定扰动项后的生物经济系统的H?保性能控制分析。具体研究工作如下:(1)介绍了本文的研究背景,其中包括现如今外来物种的入侵情况、原因及影响,先着重分析了外来物种入侵下的鱼类种群生存和捕捞情况;其次介绍了生物控制分析方法,包括分阶段结构的Holling IV系统的分析、时滞系统的Hopf分岔分析、生物系统的保性能控制分析;然后,简述了外来物种和广义生物系统的研究进展;最后,介绍了本文的主体内容。(2)研究了外来物种入侵下的具捕食关系的一种带有Holling IV的分阶段结构的非自治捕食系统,基于两种基础增长模型,得到生物捕食模型。然后通过分析验证,得出一组使系统永久性存在的充分条件,即满足该条件的情况下,可达到生态系统中所涉及物种的长久共存的状态,通过仿真例子给出说明。(3)研究了外来物种入侵下的具抑制关系的一种时滞分阶段结构的生物经济系统。本文使用适当的参数化和线性化方法,运用中心流形和庞加莱标准型办法,分析了时滞广义系统Hopf分岔的方向、稳定性及周期性,仿真算例验证了所得结论的正确性。(4)研究了外来物种入侵下的具竞争关系的一种分阶段结构的广义生物经济系统的保性能控制问题。从人工捕获收益、对外来物种的净化能力入手,建立广义系统模型,讨论平衡点附近的性质,然后通过T-S模糊方法建立广义线性生物模型,在此基础上添加受自然因素影响的满足Lipschitz条件的扰动项,确定性能指标,用LMI方法给出简化的不确定广义系统保性能控制器存在的充分条件,仿真数例验证了研究结果的有效性。
[Abstract]:Biological mathematics is applied mathematical thinking, trying to solve the biological problems from the mathematical perspective, alien species invasion often damage the local ecosystem and geographical structure, The biological mathematics is used to study the ecosystem of alien species invasion, to understand the economic production and the dynamic behavior of the population, This paper, based on the invasion of alien species, introduces the ecosystem of three different biological relationships, including predator relationship, inhibition relationship and competition relationship, which can play a positive role in the stability and development of human society. First, according to the predator-prey relationship between alien species and species in the original ecosystem, a permanent analysis of the ecosystem with functional response function is carried out on the basis of the predator-prey relationship between alien species and species in the original ecosystem. Based on the generalized bio-economic theory and the situation that the invasive species release chemical substances to affect the local species and the local species show time-delay variation, the Hopf bifurcation and equilibrium periodic analysis of the time-delay biological model with a phased structure are carried out. Finally, the periodic analysis of the equilibrium point is given. Considering the competitive relationship between alien species and native species, the H? Analysis of guaranteed cost control. The specific research work is as follows: (1) introduce the research background of this paper, including the invasion of alien species nowadays, the reasons and effects, and analyze the survival and fishing situation of the fish population under the invasion of alien species. Secondly, the biological control analysis methods are introduced, including the analysis of the Holling IV system with phased structure, the Hopf bifurcation analysis of the time-delay system, the guaranteed cost control analysis of the biological system, and the research progress of the alien species and the generalized biological system. Finally, this paper introduces the main content of this paper. (2) A non-autonomous predator-prey system with a phased structure of Holling IV is studied under the invasion of alien species, based on two basic growth models. The biological predator model is obtained. Then, by analysis and verification, a set of sufficient conditions for the permanent existence of the system are obtained, that is, if the condition is satisfied, the species involved in the ecosystem can coexist for a long time. A simulation example is given to illustrate how to study a time-delay, phased structure bio-economic system with suppression relationship under alien species invasion. In this paper, appropriate parameterization and linearization methods are used. The direction, stability and periodicity of Hopf bifurcation for singular systems with time delay are analyzed by means of the central manifold and the Poincare canonical form method. A simulation example is given to verify the correctness of the conclusions obtained. (4) the guaranteed cost control problem of a phased structure of generalized bio-economy system with competitive relationship under invasive alien species is studied. Based on the purification ability of alien species, the generalized system model is established, and the properties near the equilibrium point are discussed. Then the generalized linear biological model is established by T-S fuzzy method. On this basis, the perturbation terms which satisfy the Lipschitz condition are added, and the performance index is determined. By using the LMI method, the sufficient conditions for the existence of guaranteed cost controllers for uncertain singular systems are given. Several examples are given to verify the validity of the results.
【学位授予单位】:沈阳工业大学
【学位级别】:硕士
【学位授予年份】:2017
【分类号】:O175

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