Structures of chaos in open reaction systems

Dynamical analysis of a periodically forced chaotic chemical oscillator

We present a comprehensive dynamical analysis of a chaotic chemical model referred to as the autocatalator, when subject to a periodic administration of one substrate. Our investigation encompasses the dynamical characterization of both unforced and forced systems utilizing isospikes and largest Lyapunov exponents-based parameter planes, bifurcation diagrams, and analysis of complex oscillations. Additionally, we present a phase diagram showing the effect of the period and amplitude of the forcing signal on the system's behavior. Furthermore, we show how the landscapes of parameter planes are altered in response to forcing application. This analysis contributes to a deeper understanding of the intricate dynamics induced by the periodic forcing of a chaotic system.

Pressure and Light Multi-Physics Fields Comodulate the Multi-Length Scales of Chemical Wave Propagation in Diffusion-Fed Gels

During plant growth, the combined effects of multi-physics fields such as light, temperature, and material concentration create a complex multi-length scales phenomenon. However, the mechanism of multi-physical field interactions on biological multi-length scales has not been thoroughly investigated. In this paper, an open diffusion-fed system is constructed by coupling gels with a Belousov-Zhabotinsky (BZ) chemical reaction system. The multi-length scales propagation of chemical waves in the gel system under the combined effect of multi-physical fields such as light (I) and pressure (ΔP) is investigated. It is found that when 85 Pa ≤ ΔP ≤ 100 Pa or 200 μW·cm^-2 ≤ I ≤ 300 μW·cm^-2, the complexity of the multi-length scales periodic structure of chemical waves shows a nonlinear change with increasing light intensity or pressure. Beyond this range, the complexity of the chemical wave multi-length scales periodic structure decreases linearly on enhancing the light intensity or increasing the pressure.

Intermittent Chaos in the CSTR Bray-Liebhafsky Oscillator-Specific Flow Rate Dependence

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.

Reexamination of gas production in the Bray-Liebhafsky reaction: what happened to O2 pulses?

Results of high-precision measurements of gas production in the BL reaction are presented, and an efficient kinetic model for their analysis is proposed. Based on this model, the data have been examined pulse by pulse, and for the first time, the entire records of gas production could be successfully reduced to series of just a few key parameters. It has been confirmed that the kinetics of O2(g) production is of the first order with respect to its precursor. Overall, only two steps have been found necessary to fit the observed pulses in gas production. The first step produces the precursor of the recorded O2(g), and its rate has two components. One component provides the peaks, and its approximation in the form of Gaussian functions has been found as satisfactory. The other component provides the constant baseline of gas production between the pulses. Finally, the precursor gives rise to O2(g) in the second step, and the simple first-order kinetics suggests that the precursor is otherwise relatively unreactive, making O2(aq) a logical candidate. However, the rate constant of this process showed almost perfect linearity with the actual concentrations of H2O2, and it was affected only little by variations in the rate of stirring. It thus seems possible that this final step in gas production, responsible for the majority of O2 produced in pulses, might not be the interphase transport O2(aq) → O2(g), as expected. Instead, it might be a truly chemical process, giving rise to O2(g) in a reaction of H2O2 with another precursor, which is not involved significantly in any other process, but it is not O2(aq). If this is true, the second-order rate constant of this process in the system with initial composition of 0.360 M KIO3, 0.345 M H2O2, and 0.055 M HClO4 at 60 °C would be 0.25-0.30 M(-1)·s(-1), depending on the rate of stirring.

Mixed mode and sequential oscillations in the cerium-bromate-4-aminophenol photoreaction

Cerium was introduced to the bromate-aminophenol photochemical oscillator to implement coupled autocatalytic feedbacks. Mixed mode and sequential oscillations emerged in the studied system, making it one of the few chemical oscillators known to support consecutive bifurcations in a batch system. The complex reaction behavior showed a strong dependence on the intensity of illumination supplied to the system. Removal of illumination during an oscillatory window affected both the frequency and amplitude of the oscillation but did not fully extinguish them, indicating that the cerium-bromate-4-aminophenol oscillator was photosensitive rather than photo-controlled. A moderate light intensity allowed for a slow evolution of the system, which proved to be critical for the emergence of transient complex oscillations. Variation of individual reaction parameters was carried out, which indicated that the development of complex oscillations occur in a narrow region and a phase diagram in the 4-aminophenol and sulfuric acid plane demonstrated this. Simulations provide strong support that transient complex oscillations observed experimentally arise from the coupling of two autocatalytic cycles.