【作者】 褚效中；

【导师】 贺占博；

【作者基本信息】 天津大学 ， 物理化学， 2004， 硕士

【摘要】 本文比较系统地研究了化学振荡领域中的数学方法、程序软件及其机理模型的进展状况，并在这些研究的基础上提出了两个新的模型来模拟相应的振荡反应体系，最后对化学振荡的共性模型进行了探索与讨论。全文共分六个部分。 第一部分总结了已应用于化学振荡研究领域的数学方法和程序软件。其中在数学方法部分主要介绍了两种常用于求解化学振荡反应数学模型的吉尔（Gear）法和龙格-库塔(Runge-Kutta)法及其优缺点，并简要描述了三种研究化学振荡反应机理模型的数学分析方法—稳定性分析、灵敏度分析和主成分分析。同时结合作者的实践，给出了用两种功能强大的符号型数学运算软件—Mathematica 和Maple 来求解振荡反应数学模型的方法。文章还简要介绍了用来模拟化学振荡机理的遗传算法和蒙特卡罗（Monte Carlo）算法以及 MECHEM 和 Chemical KineticSimulator（CKS）软件。 第二部分比较详细地总结了化学振荡机理和模型的研究进展，其主要包括以下方面的内容：（1）化学振荡的理论基础：非线性热力学及其数学背景，化学振荡的动力学分析理论—稳定性理论、分岔理论与涨落理论。（2）化学振荡机理和模型的研究状况。（3）讨论了该领域研究的特点和存在的问题，并展望了进一步发展的方向。（4）最后介绍了选题的意义。 文章的第三部分给出了一个用 C 语言编写的变步长的龙格-库塔(Runge-Kutta)来求解化学振荡模型中的非线性微分方程组的算法程序。该程序克服了以往龙格-库塔程序不能变步长的缺点，并且其求解动力学微分方程组的能力大大加强。 文章的第四、五部分详细地研究了 BR(Briggs—Rauscher)振荡反应体系与BL（Bray—Liebhafsky）振荡反应体系的特点与存在的问题，并从元素电极电势图角度分别对两个振荡体系提出了新的反应机理及其模型。新的数学模型能够较好的模拟和解释相应振荡体系的实验现象，尤其是新的数学模型能解释与模拟一些以前相关的模型所没有模拟过的实验现象。 文章的第六部分对化学振荡的共性模型进行了探索与讨论，并在研究两个变量振荡模型的基础上构造了一个三个组分变量和一个四个组分变量且不含有自催化步骤的简单化学振荡模型，并对相应的数学模型进行了数学分析与计算机模拟。更多还原

【Abstract】 Mathematical methods, programs, software, reaction mechanisms and models inthe field of chemical oscillation are studied systematically. And two models ofchemical oscillating reaction and the corresponding mathematical models aredeveloped for the corresponding oscillation system, respectively. Finally, commonmodels of chemical oscillatory reaction are also dealt with. The thesis includes sixchapters. In the first section, mathematical methods and computer software applied to thefield of chemical oscillation are summarized. The contents discussed are as follows:the advantages and disadvantages of Gear method and Runge-Kutta method in solvingoscillation models; three mathematical analysis methods, i.e., stability analysis,sensitivity analysis and principal component analysis; Two powerfulsoftware—Mathematica and Maple are introduced according to the authors’ practice.Additionally, two algorithms—Genetic Algorithm and Monte Carlo Algorithm as wellas two software—MECHEM and Chemical Kinetic Simulator used in modelingmechanisms of chemical oscillations is also dealt with briefly. In the section II, the progress of mechanisms and models of chemical oscillationis summarized in detail. The main contents are discussed as follows: (1)thefundamental theories of chemical oscillation include nonlinear thermodynamics, thebackground of mathematics and the kinetic analytic theories－the theory of stability,the theory of bifurcation and the theory of fluctuation. (2) the situation of study onmechanisms and models of chemical oscillation. (3) some features and problems inthis field are discussed, and the tendency of development is reviewed. (4) Finally, thesignificance of selected topic is introduced. In the section III, a Runge—Kutta algorithm of adjusting steps and thecorresponding C program are given to solve nonlinear ordinary differential equations,which can overcome the disadvantage of not controlling calculating steps. In the section IV and V, Brig—Rauscher oscillatory reaction and Bray—Liebhafsky oscillatory reaction are studied in detail. Furthermore, the reactionmechanism and the corresponding mathematical model are established for these twooscillating systems, respectively. The results of simulation are in good agreement withthe relevant experimental phenomena. Especially, the new mathematical model can<WP=5>simulate some experimental phenomena that had not been modeled in thecorresponding oscillating system. In the section VI, common models of chemical oscillation are discussed. Andbased on the study of two-variable oscillatory model, a three-variable and afour-variable chemical oscillating models are developed, which do not includeautocatalysis steps. Additionally, some corresponding mathematical analysis,computations and simulations on them are studied in detail.更多还原