Investigation of Dynamic Behavior of the Bray−Liebhafsky Reaction in the CSTR. Determination of Bifurcation Points

Abstract

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.

New type of the source of travelling impulses in two-variable model of reaction–diffusion system

“…It is not excluded that the target patterns can appear in the BrayLiebhavsky reaction for which the model describing all observed time patterns has been elaborated by the Belgrade group [43,44].…”

Stochastic transitions between attractors in a tristable thermochemical system: competition between stable states

“…However, it is much more difficult task to find a tristable system. Constructing the system with three attractors one has to realize that only two of them can be stationary states, because the nullclines (5,6) can be have at most three intersection points, one of which must be then a saddle point. Another important indication follows from the stability analysis (which can be based on linear dynamics), according to which a stationary state located on the repulsive branch of a T ultimately becomes unstable for sufficiently high q.…”

“…These prominent changes appear in far-from-equilibrium systems, close to bifurcations leading to new dynamical regimes specific for nonequilibrium conditions, like excitability, simple and complex oscillations, and multistability. The BelousovZhabotinsky [3,4] and Bray-Liebhavsky [5,6] reactions are the best known examples of chemical systems exhibiting a rich variety of nonlinear phenomena. Fluctuations also attract considerable attention since their positive, constructive role has been revealed in the phenomena of stochastic and coherence resonances [7][8][9][10], analyzed theoretically [11,12] and observed in experiments [13,14] as well.…”

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

“…The first of our results were related to the phenomenological studies of their dynamic behaviours and reaction kinetics (Anić et al 1985;Anić et al 1986a;Anić et al 1986b;Anić et al 1987;Anić et al 1988;Anić et al 1989a;Anić et al 1989b;Anić et al 1991;Anić et al 1996;Anić. 1997a;Anić et al 1997b;Anić et al 1998;Anić et al 2007;Anić et al 2009;Blagojević 2000;Blagojević et al 2008;Blagojević et al 2009;Ćirić et al 2000;Milenković et al 2012;Radenković 1997;Stanisavljev et al 1995;Stanisavljev 1997;Stanisavljev et al 1998a;Stanisavljev et al 1998b;Stanisavljev et al 2002;Stanisavljev et al 2011;Vukojević et al 2000;Vukojević et al 2002). Furthermore, various methods were developed for formal kinetics of homogenous oscillatory process (Anić et al 1986a;Anić et al 1987;Anić et al 1988;Anić et al 1996;Anić et al 2007), as well as for the stability analysis of the postulated models (Kolar- Anić et al 1995b;Schmitz et al 2000).…”