Belousov-Zhabotinsky reaction dynamics

An example of the application of J2-weighted imaging is afforded by the imaging of the dynamics of chemical waves in the Belousov-Zhabotinsky reaction shown in figure B 1.14.5 [16]. In these images, bright... 

P.De Kepper and K.Bar-Eli, Dynamical Properties of the Belousov-Zhabotinski Reaction in a Flow System. Theoretical and Experimental Analysis, The Journal of Physical Chemistry, 87,480-488(1983). 

We have seen that the Belousov-Zhabotinsky reaction, even in the restricted parameter range for which some elementary analysis can be done, has a large variety of behaviors, which makes it the ideal model system to illustrate nonlinear dynamics of chemical systems. We briefly mention here a kinetic system of a rather different origin, the FitzHugh-Nagumo (FN) model (Murray, 1993 Meron, 1992) ... 

A. L. Belmonte, Q. Ouyang, and J.-M. Flesselles. Experimental Survey of Spiral Dynamics in the Belousov-Zhabotinsky Reaction. Journal de Physique II, 7 1425-1468, 1997. 

Reducing the dynamics of a complex system to that of a two-variable system is the goal pursued in most studies devoted to periodic or excitable behaviour, in chemistry as in biology. The main impetus for such a reduction is that it allows us to study these phenomena by means of phase plane analysis. The latter clarifies the origin of the two modes of dynamic behaviour, and highlights basic features common to different systems. This approach was followed in the study of excitability and oscillations in the Belousov-Zhabotinsky reaction (Tyson, 1977), and in... 

Roux, J.C. 1993. Dynamical systems theory illustrated chaotic behavior in the Belousov-Zhabotinsky reaction. In Chaos in Chemistry and Biochemistry. R.J. Field L. Gyorgyi, eds. World Scientific, Singapore, pp. 21-46. 

It is well known that the Belousov-Zhabotinsky (BZ) reaction can initiate free radical polymerisation (2) while it is less known that polymers can also affect the dynamics of the BZ reaction. Recently, we have performed preliminary experiments perturbing the BZ reaction with two different water-soluble nonionic polymers containing alcoholic end-groups, namely polypropylene glycol and polyethylene glycol (PEG) (i). It was realized that the Belousov-Zhabotinsky reaction responded to the perturbation in an unexpected way. Thus, a systematic study was undertaken to inquire whether the perturbation effect can be attributed exclusively to PEG reactive endgroups (here primary alcoholic groups) or the chemical nature of polymeric backbone plays also a relevant role. 

Fig. 4. The state transition diagram found for the Field-Noyes mechanism for the Belousov-Zhabotinsky reaction by Hastings and Murray,and for feedback inhibition. The dynamics of an equation with this structure is discussed in Sections 4.1 and 4.2.

Dynamic Regimes of the Belousov-Zhabotinsky Reaction According to the Oregonator Kinetic Model... 

Chemical systems with complex kinetics exhibit a fascinating range of dynamical phenomena. These include periodic and aperiodic (chaotic) temporal oscillation as well as spatial patterns and waves. Many of these phenomena mimic similar behavior in living systems. With the addition of global feedback in an unstirred medium, the prototype chemical oscillator, the Belousov-Zhabotinsky reaction, gives rise to clusters, i.e., spatial domains that oscillate in phase, but out of phase with other domains in the system. Clusters are also thought to arise in systems of coupled neurons. 

Jahnke, W. Skaggs, W. E. Winfree, A. T. 1989. Chemical Vortex Dynamics in the Belousov-Zhabotinsky Reaction and in the Two-Variable Oregonator Model, J. Phys. Chem. 93, 740-749. 

Plesser, T. Muller, S. C. Hess, B. 1990, Spiral Wave Dynamics as a Function of Proton Concentration in the Ferroin-Catalyzed Belousov-Zhabotinsky Reaction, J. Phys. Chem. 94, 7501-7507. 

Su, S. Menzinger, M. Armststrong, R. L. Cross, A. Lemaire, C. 1994. Magnetic Resonance Imaging of Kinematic Wave and Pacemaker Dynamics in the Belousov-Zhabotinsky Reaction, J. Phys. Chem. 98, 2494-2498. 

Maeda, S., Hara, Y., Yoshida, R., and Hashimoto, S. (2008) Control of dynamic motion of a gel actuator driven by the Belousov-Zhabotinsky reaction. Macromol. Rapid Commun., 29, 401-405. 

One important feature of reaction-diffusion fields, not shared by fluid dynamical systems as another representative class of nonlinear fields, is worth mentioning. This is the fact that the total system can be viewed as an assembly of a large number of identical local systems which are coupled (i.e., diffusion-coupled) to each other. Here the local systems are defined as those obeying the diffusionless part of the equations. Take for instance a chemical solution of some oscillating reaction, the best known of which would be the Belousov-Zhabotinsky reaction (Tyson, 1976). Let a small element of the solution be isolated in some way from the bulk medium. Then, it is clear that in this small part a limit cycle oscillation persists. Thus, the total system may be imagined as forming a diffusion-coupled field of similar limit cycle oscillators. 

As // increases further, the system may show more and more complicated dynamics through a number of bifurcations. It may show complicated periodic oscillations, quasi-periodic oscillations or a variety of non-periodic behaviors. For instance, we know of the recent discoveries of fantastic bifurcation structures in the spatially homogeneous Belousov-Zhabotinsky reaction, see Hudson et al., 1979. 

Survey of Spiral Dynamics in the Belousov Zhabotinsky Reaction. 

Another type of dynamic self-organization, so-called dissipative structure , is known as a general physical phenomenon which is generated under chemical or physical conditions far from equilibrium [238]. Many spatiotemporal patterns of the dissipative structures are formed in the dissipative processes ranging in size from sub-micrometers to hundreds of kilometers. Several types of regular patterns, e.g. spirals in the Belousov-Zhabotinsky reaction systems, the honeycomb and stripes of Rayleigh/Benard convection, are formed as spatiotemporal patterns in the dissipative processes. To utilize the dissipative structures for self-organization of molecular assemblies, the spatiotemporal patterns have to be frozen as stationary stable structures. 

Li N, Zhao JP, Wang JC (2008) Complex dynamics and enhanced photosensitivity in a modified Belousov-Zhabotinsky reaction. J Chem Phys 128 244509... 

Rossi, F., Vaxsalona, R., Liveri, M.L.T. New features in the dynamics of a ferroin-catalyzed Belousov-Zhabotinsky reaction induced by a zwitterionic surfactant. Chem. Phys. Lett. 463(4-6), 378-382 (2008)... 

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