论文标题
Belousov-Zhabotinsky反应模型的修订动力学
Revised dynamics of the Belousov-Zhabotinsky reaction model
论文作者
论文摘要
本文的主要目的是检测Belousov-Zhabotinsky化学反应的Györgyi-Field模型的动力学特性。给出的相应的三变量模型作为一组非线性普通微分方程取决于一个参数，即流速。由于此参数的某些值会引起混乱，因此进行了分析以识别不同的动态制度。使用经典和新技术对动态特性进行了验证和量化。也就是说，相肖像，分叉图，傅立叶光谱分析，混乱的0-1测试以及近似熵。观察并详细描述了混乱的近似熵与0-1测试之间的相关性。此外，在每个级别上，计算了混乱和近似熵的0-1测试的流速的三阶段系统，都显示出相同的模式。该研究导致一个开放的问题，一组流量参数是否具有类似cantor的结构。
The main aim of this paper is to detect dynamical properties of the Györgyi-Field model of the Belousov-Zhabotinsky chemical reaction. The corresponding three-variable model given as a set of nonlinear ordinary differential equations depends on one parameter, the flow rate. As certain values of this parameter can give rise to chaos, the analysis was performed in order to identify different dynamics regimes. Dynamical properties were qualified and quantified using classical and also new techniques. Namely, phase portraits, bifurcation diagrams, the Fourier spectra analysis, the 0-1 test for chaos, and approximate entropy. The correlation between approximate entropy and the 0-1 test for chaos was observed and described in detail. Moreover, the three-stage system of nested subintervals of flow rates, for which in every level the 0-1 test for chaos and approximate entropy was computed, is showing the same pattern. The study leads to an open problem whether the set of flow rate parameters has Cantor like structure.
