几类生物学模型的复杂性行为研究毕业论文.docVIP

论文题目 几类生物数学模型的复杂性行为研究 系 别 专 业 数学与应用数学 班 级 学 号 学生姓名 指导教师 完成时间 年 月 摘要 本文考虑了生态学中几个经典数学模型的改进和推广,利用微分方程稳定性理论和数值分析, 研究其动力学行为, 并探讨了系统中参数对其动力学行为的影响, 为解释、预测和控制生态学中的一些现象提供相应的理论依据。具体地，本文做了以下工作: 第一章，简介微分方程稳定性理论的基本知识。 第二章，借助特征值判别法、 Lyapunov函数和微分不等式，细致地分析和讨论单种群生物模型的优缺点及平衡点的稳定性，获得了单种群生物模型稳定性的充要条件。 第三章，运用特征值判别法、 Lyapunov函数、微分不等式及计算机数值模拟，精细地分析和讨论两种群竞争模型的优缺点，并对模型进行改进，使得模型与实际更加贴近，最后得出了两种群相互竞争模型稳定性的相关条件。同时在改进过程中，得出了一元四次方程实根个数的判别方法。此外，理论研究结果与两个种群相互竞争模型的SIMLINK仿真数值结果十分吻合。 关键词： 生态学； 微分方程； 稳定性； SIMLINK仿真 Complex Dynamics in Several Mathematical Models Abstract This thesis is focus on the improvement and popularization of several classical mathematic model in the ecology. Researching on its dynamic behaviors by using numerical analysis and theory of differential equation stability. As well as discussing the influence of parameters in system on the dynamic behaviors. All these have provide corresponding theoretical basis when we interpret ,predict, and control some phenomena in the ecology. Below are what this thesis has done in details： Chapter one , Stability theory for differential equation of the paper are presented. Chapter two, using Eigenvalue method, Lyapunov function and Differential Inequality. We analyze and discuss the advantages and disadvantages of single population biology model and stability of the equilibrium point, obtaining the sufficient condition of the stability of single population biology model . Chapter three, using Eigenvalue method, Lyapunov function, Differential Inequality and Computer numerical simulation. We analyze and discuss the advantages and disadvantages of the two population competition model .At the same time improving the model and make it more consistent with the actual, obtaining the related conditions of two populations competition model.In the improvement process, obtaining the number of roots for quartic equation. In a