deangelis模型的动力学分析毕业论文.doc
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deangelis模型的动力学分析毕业论文,摘要种群动力学已发展为生物数学的一个非常重要的分支学科，它在生态学理论中，特别是动植物保护和生态环境的治理与开发等领域都有着非常重要的作用。生物学家针对种群的相互作用关系进行大量的实验，并对实验数据进行统计分析以及合理细致的机理分析，建立微分、积分或者差分方程形式的数学模型，以用来描述、预测、调节和控制物种的发展过程和...
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摘 要
种群动力学已发展为生物数学的一个非常重要的分支学科，它在生态学理论中，特别是动植物保护和生态环境的治理与开发等领域都有着非常重要的作用。生物学家针对种群的相互作用关系进行大量的实验，并对实验数据进行统计分析以及合理细致的机理分析，建立微分、积分或者差分方程形式的数学模型，以用来描述、预测、调节和控制物种的发展过程和发展趋势.数学家用数学的理论和方法针对所建立的数学模型，研究生态系统中种群的长期变化规律，得到一些理论上的结果,再用来解释和解决具体的生物学问题。这对于研究生态学有重要意义，可以使人们更好的认识自然。
自然界中的生态系统是多种多样的，常见的有单食物链模型，竞争模型。数学上常用常微分方程组，偏微分方程组，时滞微分方程组等描述.对模型主要考虑的问题有:系统正平衡解(周期解)的存在性，平衡解的局部和全局稳定性、系统的一致持续生存等性质。常用的理论有:微分方程(组)的定性理论,分歧理论,不动点指数和拓扑度理论。本文通过对DeAngelis模型解的研究来表现种群之间的关系。
文中主要研究该模型的平衡点与极限环，结合生态规律对捕食者-食饵模型进行分析。
关键词 平衡点 捕食者-食饵模型 局部渐近稳定性
Abstract
Population dynamics has been developed as a bio-mathematical a very important branch of science, theory in ecology, especially the flora and fauna protection and the ecological environment in areas such as governance and development are a very important role. Biologist for the populations a great deal of interaction between the experimental and statistical analysis of experimental data as well as a reasonable mechanism of detailed analysis, differential, integral or differential equation forms of the mathematical model to describe, predict, regulate and control the development of species and the development of trend. mathematician with mathematical theories and methods for the mathematical model created to study the ecosystem of the long-term population changes of some theoretical results, and then used to explain and address specific biological issues. This is the study of ecology are important, you can make people a better understanding of the natural. At present, the population has become a mathematical model for the development of resources, a more rational use of resources and environmental protection an important tool.
Natural ecosystems in a variety of common single-food chain model, competition model. Mathematical common ordinary differential equations, partial differential equations, delay differential equations to describe groups. To model the main issues to consider : system is a balanced solution (of periodic solutions) the existence of equilibrium solution of the local and global stability, the continued survival of the system, such as the nature of consensus. the theory of commonly used are: differential equations (Unit) of the qualitative theory, differences between the theory of fixed point index and the topological degree theory.
In this paper,wo know the model’s Equilibrium point and Limited annulus,combine the rule of zoology to study the Predator - Prey Model.
Key words Equilibrium point Predator - Prey Model Local asymptotic stabilit
目 录
摘 要 I
ABSTRACT II
第1章 绪 论 1
1.1 引 言 1
1.2 课题研究背景与目的 4
1.2.1 研究背景 4
1.2.2 研究目的 5
第2章 预备知识 8
2.1平衡点的定义 8
2.2极限环的定义 9
第3章 平衡点与极限环的讨论 10
3.1正平衡点的讨论 10
3.2平面线性系统平衡点分类 12
3.3极限环的讨论 16
第4章 数值模拟及主要结果的生态学意义 18
4.1数值模拟 18
4.2主要结果的生态学意义 20
总 结 21
致 谢 22
参 考 文 献 23
附 录1 24
附 录2 28
附 录3 33
种群动力学已发展为生物数学的一个非常重要的分支学科，它在生态学理论中，特别是动植物保护和生态环境的治理与开发等领域都有着非常重要的作用。生物学家针对种群的相互作用关系进行大量的实验，并对实验数据进行统计分析以及合理细致的机理分析，建立微分、积分或者差分方程形式的数学模型，以用来描述、预测、调节和控制物种的发展过程和发展趋势.数学家用数学的理论和方法针对所建立的数学模型，研究生态系统中种群的长期变化规律，得到一些理论上的结果,再用来解释和解决具体的生物学问题。这对于研究生态学有重要意义，可以使人们更好的认识自然。
自然界中的生态系统是多种多样的，常见的有单食物链模型，竞争模型。数学上常用常微分方程组，偏微分方程组，时滞微分方程组等描述.对模型主要考虑的问题有:系统正平衡解(周期解)的存在性，平衡解的局部和全局稳定性、系统的一致持续生存等性质。常用的理论有:微分方程(组)的定性理论,分歧理论,不动点指数和拓扑度理论。本文通过对DeAngelis模型解的研究来表现种群之间的关系。
文中主要研究该模型的平衡点与极限环，结合生态规律对捕食者-食饵模型进行分析。
关键词 平衡点 捕食者-食饵模型 局部渐近稳定性
Abstract
Population dynamics has been developed as a bio-mathematical a very important branch of science, theory in ecology, especially the flora and fauna protection and the ecological environment in areas such as governance and development are a very important role. Biologist for the populations a great deal of interaction between the experimental and statistical analysis of experimental data as well as a reasonable mechanism of detailed analysis, differential, integral or differential equation forms of the mathematical model to describe, predict, regulate and control the development of species and the development of trend. mathematician with mathematical theories and methods for the mathematical model created to study the ecosystem of the long-term population changes of some theoretical results, and then used to explain and address specific biological issues. This is the study of ecology are important, you can make people a better understanding of the natural. At present, the population has become a mathematical model for the development of resources, a more rational use of resources and environmental protection an important tool.
Natural ecosystems in a variety of common single-food chain model, competition model. Mathematical common ordinary differential equations, partial differential equations, delay differential equations to describe groups. To model the main issues to consider : system is a balanced solution (of periodic solutions) the existence of equilibrium solution of the local and global stability, the continued survival of the system, such as the nature of consensus. the theory of commonly used are: differential equations (Unit) of the qualitative theory, differences between the theory of fixed point index and the topological degree theory.
In this paper,wo know the model’s Equilibrium point and Limited annulus,combine the rule of zoology to study the Predator - Prey Model.
Key words Equilibrium point Predator - Prey Model Local asymptotic stabilit
目 录
摘 要 I
ABSTRACT II
第1章 绪 论 1
1.1 引 言 1
1.2 课题研究背景与目的 4
1.2.1 研究背景 4
1.2.2 研究目的 5
第2章 预备知识 8
2.1平衡点的定义 8
2.2极限环的定义 9
第3章 平衡点与极限环的讨论 10
3.1正平衡点的讨论 10
3.2平面线性系统平衡点分类 12
3.3极限环的讨论 16
第4章 数值模拟及主要结果的生态学意义 18
4.1数值模拟 18
4.2主要结果的生态学意义 20
总 结 21
致 谢 22
参 考 文 献 23
附 录1 24
附 录2 28
附 录3 33
