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Feedback driven by enzyme catalyzed reactions occurs widely in biology and has been well characterized in single celled organisms such as yeast. There are still few examples of robust enzyme oscillators in vitro that might be used to study nonlinear dynamical behavior. One of the simplest is the urea-urease reaction that displays autocatalysis driven by the increase in pH accompanying the production of ammonia. A clock reaction was obtained from low to high pH in batch reactor and bistability and oscillations were reported in a continuous flow rector. However, the oscillations were found to be irreproducible and one contributing factor may be the lack of stability of the enzyme in solution at room temperature. Here, we investigated the effect of immobilizing urease in thiol-poly(ethylene glycol) acrylate (PEGDA) hydrogel beads, prepared using emulsion polymerization, on the ureaurease reaction. The resultant mm-sized beads were found to reproduce the pH clock and, under the conditions employed here, the stability of the enzyme was increased from hours to days.

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An intriguing step of the Bray−Liebhafsky oscillatory reaction, that is, iodine oxidation with hydrogen peroxide, was examined. This process is characterized by enormous stochasticity of reaction induction times in the presence of mild mixing. In the present investigations, it was found that even in the presence of mixing, stochasticity is seriously reduced with simple glass powder addition. Using transparent glass, standard deviations changed from 184.9 to 10.6 min for 19 °C, and from 128.2 to 1.9 min for 27 °C. Repeating experiments with amber glass further confirmed those results as standard deviations changed from the mentioned ones to 8.7 min for 19 °C and to 2.5 min for 27 °C. Inert glass particles enhanced heterogeneous nucleation of oxygen formed in chemical reactions. Together with the previous analysis of the involved kinetic barrier of the whole reaction, it is an additional strong evidence of a possible energetic coupling between nucleation of glass cavities and chemical reactions. Such processes are usually neglected and may considerably change the investigations of the reaction mechanisms in other complex systems. Reaction was followed by the potentiometric method at 19 and 27 °C. The adjusted stopped-flow titration method was used in order to confirm the high degree of iodine to iodate conversion in the presence of nucleation centers.

A physicochemical model of iodine oxidation with hydrogen peroxide is extended by heterogeneous processes, conceptually improving the understanding of the reaction mechanism.

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.

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The intermittency or intermittent bursting as the type of dynamic state when two qualitatively different behaviors replace one another randomly during the course of the reaction, although all the control parameters remain constant, is found in the BriggsRauscher oscillating system moderated by a very small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude is diminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts of oscillations. For the concentrations used here, the range of phenol concentrations where intermittent bursting oscillations occur in a closed reactor is ca. 1.8×10−5 to 3.6×10−5 M. Bursting also occurs in an open reactor and can be sustained indefinitely at 5.53×10−5 M concentration. The intermittent bursting behavior is robust, and can be achieved at a variety of conditions.