Studies Of Reaction Mechanisms And Models Of Chemical Oscillation

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 cansimulate 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.