一类双变量化学振荡反应方程的极限环求解

doi:10.16088/j.issn.1001-6600.2024101407

广西师范大学学报（自然科学版） ›› 2025, Vol. 43 ›› Issue (5): 167-174.doi: 10.16088/j.issn.1001-6600.2024101407

一类双变量化学振荡反应方程的极限环求解

王麟¹, 汪海玲^2*

1.广西师范大学物理与科学技术学院, 广西桂林 541004;
2.广西师范大学数学与统计学院, 广西桂林 541006

收稿日期:2024-10-14 修回日期:2024-11-20 出版日期:2025-09-05 发布日期:2025-08-05
通讯作者: 汪海玲(1980—), 女, 湖北黄冈人, 广西师范大学教授, 博士。 E-mail: wanghl@gxnu.edu.cn
基金资助:
国家自然科学基金(12461099); 广西科技基地和人才专项项目(桂科AD23026220)

Solution of Limit Cycles for a Class of Bivariate Chemical Oscillation Reaction Equations

WANG Lin¹, WANG Hailing^2*

1. School of Physics and Technology, Guangxi Normal University, Guilin Guangxi 541004, China;
2. School of Mathematics and Statistics, Guangxi Normal University, Guilin Guangxi 541006, China

Received:2024-10-14 Revised:2024-11-20 Online:2025-09-05 Published:2025-08-05

摘要/Abstract

摘要： 本文研究一类双变量化学振荡反应方程的极限环求解问题。为了求解这类方程, 首先将双变量化学振荡反应方程简化为一般形式的Liénard方程;然后采用摄动增量法对该方程进行极限环求解;接着以摄动阶段得到的零阶摄动解为起点, 增量阶段逐步迭代逼近, 最终得到方程的极限环;最后通过连续搅拌釜式反应器和糖酵解振荡反应的实例来验证摄动增量法, 并与数值积分法进行比较, 结果显示两者高度一致。该研究证明了摄动增量法在处理此类非线性动力学方程极限环问题中的有效性。

关键词: Liénard方程, 摄动增量法, 极限环, 连续搅拌釜式反应器, 糖酵解振荡反应

Abstract: In this paper, the problem of solving limit cycles for a class of bivariate chemical oscillation reaction equations is investigated. To solve these equations, firstly, the bivariate chemical oscillation reaction equations are simplified into a general form of Liénard equation and the perturbation increment method is used to solve limit cycles. Starting from the zero-order perturbation solution obtained during the perturbation phase, the increment phase iteratively approximates step by step until the final limit cycle is achieved. Through examples of continuous stirred tank reactor reactions and glycolysis reactions, and compared with numerical integration method, the results show a high degree of consistency, demonstrating the effectiveness of the perturbation-increment method in handling limit cycle problems of such nonlinear dynamic equations.

Key words: Liénard system, perturbation incremental method, limit cycle, continuous stirred tank reactor reactions, glycolysis reactions

中图分类号: O175

王麟, 汪海玲. 一类双变量化学振荡反应方程的极限环求解[J]. 广西师范大学学报（自然科学版）, 2025, 43(5): 167-174.

WANG Lin, WANG Hailing. Solution of Limit Cycles for a Class of Bivariate Chemical Oscillation Reaction Equations[J]. Journal of Guangxi Normal University(Natural Science Edition), 2025, 43(5): 167-174.

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一类双变量化学振荡反应方程的极限环求解

Solution of Limit Cycles for a Class of Bivariate Chemical Oscillation Reaction Equations

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