Confirmation of high flow rate chaos in the Belousov-Zhabotinskii reaction (original) (raw)
The Journal of Chemical Physics, 2009
We report a detailed numerical investigation of the relative abundance of periodic and chaotic oscillations in phase diagrams for the Belousov-Zhabotinsky ͑BZ͒ reaction as described by a nonpolynomial, autonomous, three-variable model suggested by Györgyi and Field ͓Nature ͑London͒ 355, 808 ͑1992͔͒. The model contains 14 parameters that may be tuned to produce rich dynamical scenarios. By computing the Lyapunov spectra, we find the structuring of periodic and chaotic phases of the BZ reaction to display unusual global patterns, very distinct from those recently found for gas and semiconductor lasers, for electric circuits, and for a few other familiar nonlinear oscillators. The unusual patterns found for the BZ reaction are surprisingly robust and independent of the parameter explored.
Controlling chaos in the Belousov—Zhabotinsky reaction
Nature, 1993
DETERMINISTIC' chaos is characterized by long-term unpredictability arising from an extreme sensitivity to initial conditions. Such behaviour may be undesirable, particularly for proces!ies dependent on temporal regulation. On the other hand, a chaotic !iY!item can be viewed as a virtually unlimited reservoir of periodic behaviour which may be accessed when appropriate feedback is applied to one of the system parameters 0 Feedback algorithms have now been successfully applied to stabilize periodic o!icillations in chaotic laserl, diode"', hydrodynamic4 and magnetoela!itic5 systems, and more recently in myocardial tissue6. Here we apply a mapbased, proportional-feedback algorithm7oll to stabilize periodic. Pefm.-nt _II 01 V G. Iso ~ of A1Y*8 o.n8try KoslUth L ~. PO Boa 7.
Intermittent Chaos in the CSTR Bray–Liebhafsky Oscillator-Specific Flow Rate Dependence
Frontiers in Chemistry
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 −1. 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.
Chaos Synchronization of Two Györgyi–Field Systems for the Belousov–Zhabotinsky Chemical Reaction
Mathematics
Chemical reactions with oscillating behavior can present a chaos state in specific conditions. In this study, we analyzed the dynamic of the chaotic Belousov–Zhabotinsky (BZ) reaction using the Györgyi–Field model in order to identify the conditions of the chaos behavior. We studied the behavior of the reaction under different parameters that included both a low and high flux of chemical species. We performed our analysis of the flow regime in the conditions of an open reaction system, as this provides information about the behavior of the reaction over time. The proposed method for determining the favorable conditions for obtaining the state of chaos is based on the time evolution of the intermediate species and phase portraits. The synchronization of two Györgyi–Field systems based on the adaptive feedback method of control is presented in this work. The transient time until synchronization depends on the initial conditions of the two systems and on the strength of the controllers...
Chaos in batch Belousov-Zhabotinskii systems
The Journal of Physical Chemistry, 1992
(17) One model of delayed, or activated, electron emission rata yielding an Arrhenius expression has ken derived by: Klots, C. E. Chem. Phys. Lett. 1991, 186, 73. However, it is not clear that the assumptions used in this derivation are applicable to finite negative ions, where there may be only a few or no bound excited states. The first example of a negative ion excited state is that of Cz-: Lineberger, W. C.; Patterson, T. A. Chem. Phys. k t r .
By numerical calculations based on our previously proposed model with Br 2 O intermediate spe cies we were able to simulate complex evolution of the Belousov-Zhabotinsky (BZ) reaction under batch con ditions. In the defined region of initial malonic acid concentration [MA] 0 (1.00 × 10 -3 mol dm 3 ≤ [MA] 0 ≤ 1.50 mol dm -3 ) different sequences of regular and complex periodic and aperiodic oscillations were obtained. It is noticed that the bromine evaporation significantly affects the dynamics of the reaction.
New evidence of transient complex oscillations in a closed, well-stirred belousov-zhabotinsky system
Journal of The Serbian Chemical Society, 2006
Some new experimental evidence of complex irregular oscillations in the Belousov-Zhabotinsky reaction realized in a batch reactor is presented. The results were obtained under relatively low cerium and malonic acid concentrations. One-dimensional maps were used for general discussion, and, particularly, for the influence of noise on the evolution of the oscillations.
Flow-driven instabilities in the Belousov–Zhabotinsky reaction: Modelling and experiments
Physical Chemistry Chemical Physics, 2001
The development of propagating patterns arising from the di †erential Ñow of reactants through a tubular reactor is investigated. The results from a series of experimental runs, using the BZ reaction, are presented to show how the wavelength and propagation speed of the patterns depend on the imposed Ñow velocity and the concentration of in the inÑow. A model for this system, based on a two-variable Oregonator model for BrO 3t he BZ reaction, is considered. A stability analysis of the model indicates that the mechanism for pattern formation is through a convective instability. Numerical simulations conÐrm the existence of propagating patterns and are in reasonable agreement with the experimental observations.