Bubanja Itana Nuša, Ivanović-Šašić Ana, Čupić Željko, Anić Slobodan, Kolar-Anić Ljiljana
Faculty of Physical Chemistry, University of Belgrade, Belgrade, Serbia.
Institute of Chemistry, Technology and Metallurgy, University of Belgrade, Belgrade, Serbia.
Front Chem. 2020 Oct 23;8:560274. doi: 10.3389/fchem.2020.560274. eCollection 2020.
Dynamic states with intermittent oscillations consist of a chaotic mixture of large amplitude relaxation oscillations grouped in bursts, and between them, small-amplitude sinusoidal oscillations, or even the quiescent parts, known as gaps. In this study, intermittent dynamic states were generated in Bray-Liebhafsky (BL) oscillatory reaction in an isothermal continuously-fed, well-stirred tank reactor (CSTR) controled by changes of specific flow rate. The intermittent states were found between two regular periodic states and obtained for specific flow rate values from 0.020 to 0.082 min. Phenomenological analysis based on the quantitative characteristics of intermittent oscillations, as well as, the largest Lyapunov exponents calculated from experimentally obtained time series, both indicated the same type of behavior. Namely, fully developed chaos arises when approaching to the vertical asymptote which is somewhere between two bifurcations. Hence, this study proposes described route to fully developed chaos in the Bray-Liebhafsky oscillatory reaction as an explanation for experimentally observed intermittent dynamics. This is in correlation with our previously obtained results where the most chaotic intermittent chaos was achieved between the periodic oscillatory dynamic state and stable steady state, generated in BL under CSTR conditions by varying temperature and inflow potassium iodate concentration. Moreover, it was shown that, besides the largest Lyapunov exponent, analysis of chaos in experimentally obtained intermittent states can be achieved by a simpler approach which involves using the quantitative characteristics of the BL reaction evolution, that is, the number and length of gaps and bursts obtained for the various values of specific flow rates.
具有间歇性振荡的动态状态由大量成组的大幅度弛豫振荡、其间的小幅度正弦振荡甚至静止部分（称为间隙）的混沌混合组成。在本研究中，通过特定流速的变化控制，在等温连续进料、充分搅拌的釜式反应器（CSTR）中的布雷-利布哈夫斯基（BL）振荡反应中产生了间歇性动态状态。在两个规则周期状态之间发现了间歇性状态，并且在特定流速值为0.020至0.082分钟时获得。基于间歇性振荡定量特征以及从实验获得的时间序列计算出的最大李雅普诺夫指数的唯象分析均表明了相同类型的行为。也就是说，当接近两个分岔之间某处的垂直渐近线时会出现完全发展的混沌。因此，本研究提出了布雷-利布哈夫斯基振荡反应中完全发展混沌的所述途径，作为对实验观察到的间歇性动力学的一种解释。这与我们之前得到的结果相关，即在CSTR条件下通过改变温度和流入碘酸钾浓度在BL中产生的周期性振荡动态状态和稳定稳态之间实现了最混沌的间歇性混沌。此外，结果表明，除了最大李雅普诺夫指数之外，通过一种更简单的方法也可以对实验获得的间歇性状态中的混沌进行分析，该方法涉及使用BL反应演化的定量特征，即针对不同特定流速值获得的间隙和突发的数量和长度。
