应用MATLAB分析模拟化学振荡的过程

Analyzing and modeling chemical oscillations with MATLAB

化学振荡反应作为非线性科学研究的真实典型范例,采用传统的计算机语言编程,作理论分析模拟烦琐而困难。本文建议用MATLAB功能强大的solve,jacobian,eig,ode,plot等内部函数,对Lotka-Volterra和Belousov-Zhabotinsky两个典型的化学振荡反应进行理论分析和数值模拟。结果表明MATLAB能够可靠、简便地寻找出振荡动力学区域并对化学动力学方程组数值积分,可以成为化学振荡理论研究的有力工具。

Chemical oscillations are typical and real paradigms for nonlinear dynamics investigations. However, because of the complexities of the chemical oscillation reactions, it is difficult to analyze and model chemical oscillations theoretically with traditional computer languages such as Fortran and C language. MATLAB is a high-performance language for technical computing. In this paper, two well-known chemical oscillation systems, Lotka-Voherra and Belousov-Zhabotinsky systems, are analyzed theoretically based on the linear stability theory with MATLAB. According to the chemical and physical principles, dynamic equations are built to describe the reactions in the oscillation system. Then the oscillation regions and curves of these systems are obtained with suitable MATLAB internal functions： solve is used to obtain the steady state, jacobian is employed to calculate the jacobi matrix, eig is applied to compute the eigenvalues of the jacobi matrix and ode is used to integrate the system of differential equations. Using these functions, analyzing and simulating the chemical oscillations are very easy and reliable. Moreover, function plot can plot and output the oscillation curves, which is helpful for observing the oscillation behaviors of the systems directly. MATLAB is hence considered as a powerful tool for modeling chemical oscillations as the alternative of traditional computer languages.