Intermittent chaos in the Bray–Liebhafsky oscillator. Temperature dependence

Abstract

Intermittent oscillations as a chaotic mixture of large amplitude relaxation oscillations, grouped in bursts and small-amplitude sinusoidal ones or even quiescent parts between them known as gaps, were found and examined in the Bray-Liebhafsky (BL) reaction performed in CSTR under controlled temperature variations. They were obtained in a narrow temperature range from 61.0 °C to 63.1 °C, where 61.0 °C is the critical temperature for burst emergence from the stable steady state and 63.1 °C is the critical temperature for gap emergence from regular oscillations. Since intermittencies appear gradually from the regular oscillatory state, and no hysteresis was obtained with decreasing/increasing temperature in the vicinity of these two bifurcations, a linear relationship between (τB/τ)(2) and (τG/τ)(2) (where τB, τG and τ denotes duration of bursts, gaps, and whole experiment, respectively), as a function of the temperature as the control parameter, was expected and obtained. Although these intermittent oscillations are chaotic with respect to the lengths of individual gaps as well as bursts, their deterministic behavior related to temperature was additionally established. Thus, the number of bursts or gaps per unit of time (NB/τ and NG/τ) has the form of a normal distribution function over the temperature range in the region where intermittencies are obtained. Temperature dependence of the Lyapunov exponents was also described by a function of the normal distribution form. Hence, we established some regularities in the chaotic behavior of intermittent oscillations that are common in life but difficult for determinations.

From small molecules to polymeric catalysts in the oscillatory carbonylation reaction: multiple effects of adding HI

“…Mixed-mode oscillations in pH have been observed and explained before in other systems, 26,30,32 however, due to the general complexity of the PCOC mechanism (which is not 100% established), it is difficult to confidently assign the mixed-mode oscillations in PdAc and P-Cat after addition of HI to certain reaction networks, especially since they are also observed in certain conditions (at 10 and 20 1C), when PdI 2 is used without any HI addition. Thus, further studies, including the transition to a CSTR reaction set-up, are needed to clarify the underlying mechanisms of the mixed-mode patterns.…”

“…Due to the constant change in concentration of reactant per s in a batch set-up, a CSTR is considered to be better suited for studying complex oscillatory behaviour. 30 The complex trends in oscillatory patterns are associated with the existence of two qualitatively different behaviours replacing one another during the course of the reaction, even when all the control parameters remain the same. 29 In such systems, the reaction networks (subnetworks) responsible for occurrence of small and large amplitude oscillations alternate.…”

Advances made by Belgrade's group in research of oscillatory reactions

“…When we found that our model of the BL reaction confirms the existence of the deterministic chaos in this system (Kolar- Anić et al 2004a;Kolar-Anić et al 2004b) the attention in our experimental investigation moved to even more complex oscillations (Schmitz et al 2006). Consequently, the exotic dynamic states were generated under controlled conditions in the BL system Bubanja et al 2016) and also in the BR reaction perturbed by phenol (Čupić et al 2014). As a result, the possibility to generate and control the intermittent dynamics in the BL reaction (Fig.…”

“…Methods for characterization of intermittencies were developed and deterministic nature of the phenomena is proved in both BL and BR system. In general, exotic dynamic states (Fig.3) were characterized by various mathematical techniques, starting from the Lyapunov exponents, Poincare sections, return maps, multifractal distributions, etc Pejić et al 2009;Čupić et al 2014;Ivanovo et al 2008;Ivanović et al 2009;Ivanović et al 2011;Blagojević et al 2015;Bubanja et al 2016;Čupić et al 2016a). The dynamic states and kinetics of Belousov-Zhabotinsky reaction was also examined (Blagojević et al 2008;Blagojević et al 2009).…”

Combining polymer-bound catalyst with polymeric substrate for reproducible pH oscillations in palladium-catalysed oxidative carbonylation of alkynes

“…Oscillatory reactions are considered to be a powerful avenue for a smart self-pulsatile polymeric systems, if coupled to the right pH-, redox-or thermo-responsive polymer or hydrogel for a grand number of potential biomimetic applications [1][2][3]. Of the reported oscillatory reactions [4][5][6][7][8], palladium-catalysed oxidative carbonylation (PCOC) of alkynes (Scheme 1) is attracting attention as one of the most versatile reactions, capable of producing sustained (for up to one month of monitoring) oscillations in pH, redox potential, turbidity, and heater power (measured by power compensation calorimetry), where the amplitude and period can be successfully regulated by adjusting the reactant composition or temperature [9][10][11][12][13][14][15][16].…”