Stability and slow-fast oscillation in fractional-order Belousov-Zhabotinsky reaction with two time scales
Stability and slow-fast oscillation in fractional-order Belousov-Zhabotinsky reaction with two time scales
复制标题
DOI：
10.21595/jve.2016.17197
复制
发表时间：
2016-11
影响因子：
1
通讯作者：
Jingyu Hou;Xianghong Li;Jufeng Chen
中科院分区：
文献类型：
--
作者：
Jingyu Hou;Xianghong Li;Jufeng Chen
本文研究了不同时间尺度下的分数阶别洛乌索夫- zhabotinsky （BZ）反应。基于分数阶微分方程的稳定性理论，讨论了分数阶BZ反应的两参数Hopf分岔的临界条件。通过对分数阶系统和整阶系统的比较，发现它们在一定的参数区间下表现出不同的稳定性，并且参数区间随着分数阶的变化而变大。在此基础上，首次研究了两个时间尺度耦合的分数阶BZ反应的慢快效应，发现了具有跳跃行为的Fold/Fold型慢快振荡，并用慢快动力学分析方法解释了其产生机理。分析了不同阶数对慢速振荡行为的影响及内部机理。
The fractional-order Belousov-Zhabotinsky (BZ) reaction with different time scales is investigated in this paper. Based on the stability theory of fractional-order differential equation, the critical condition of Hopf bifurcation with two parameters in fractional-order BZ reaction is discussed. By comparison of the fractional-order and integer-order systems, it is found that they will behave in different stabilities under some parameter intervals, and the parameter intervals may become larger with the variation of fractional order. Furthermore, slow-fast effect is firstly studied in fractional-order BZ reaction with two time scales coupled, and the Fold/Fold type slow-fast oscillation with jumping behavior is found, whose generation mechanism is explained by using the slow-fast dynamical analysis method. The influences of different fractional orders on the slow-fast oscillation behavior as well as the internal mechanism are both analyzed.