Experimental results obtained by operating the Bray-Liebhafsky (BL) reaction in the CSTR are presented. The dynamic behavior of the BL reaction is examined at several operation points in the concentration phase space, by varying different parameters, the specific flow rate, temperature, and mixed inflow concentrations of the feed species, one at a time. Different types of bifurcation leading to simple periodic orbits, supercritical and subcritical Hopf bifurcations, saddle node infinite period bifurcation (SNIPER), saddle loop infinite period bifurcation, and jug handle bifurcation, are observed. Moreover, complex dynamic behavior, including transition from simple periodic oscillations to complex mixed-mode oscillations and chaos, and bistability are also discovered.
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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