Oscillatory reactions spatial patterns

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

Oscillatory reactions provide one of the most active areas of research in contemporary chemical kinetics and two published studies on the photochemistry of Belousov-Zhabotinsky reaction are very significant in this respect. One deals with Ru(bpy)3 photocatalysed formation of spatial patterns and the other is an analysis of a modified complete Oregonator (model scheme) system which accounts for the O2 sensitivity and photosensitivity. ... 

In contrast to standard two-species reaction-diffusion systems, the uniform steady state of the hyperbolic reaction-diffusion system can undergo a spatial Hopf bifurcation to oscillatory spatial pattern, if A3 = 0 can be fulfilled for some % 0-This condition gives rise to a second-order polynomial in k ... 

The MA in BZ reaction has an important drawback which is producing carbon dioxide gas bubbles in the oscillating reaction process. Some attempts have been made to develop gas-free versions of the BZ reactions. The diketonic compound such as cyclohexanedione (CHD) is a well-set example in which the gas-free oscUlations and formation of spatial patterns have been examined. The acetyl acetone (AA) and ethyl acetoacetate (EAA) can also bear an analogue diketonic property. The potential oscillations in these two compounds have been reported in well-stirred medium. Though, the characteristics of an oscillating reaction in stirred reaction may differ from the unstirred reaction medium. Thus, two diketonic compounds, namely AA and EAA, are selected to extend the study of patterns formation and oscillatory behaviors in unstirred BZ conditions. 

Ertl, Jakubith, Rotermund, v. Oertzen, Cathode Lens] Ertl, Gerhard/Sven Jaku-bith/Harm Hinrich Rotermund/Alexander v. Oertzen Imaging of Spatial Pattern Formation in an Oscillatory Surface Reaction by Scanning Photoemission Microscopy, Journal of Chemical Physics 91 (1989), p. 4942-4948. 

We have seen that delayed feedback can be an efficient method for manipulation of essential characteristics of chaotic or noise-induced spatiotem-poral dynamics in a spatially discrete front system and in a continuous reaction-diffusion system. By variation of the time delay one can stabilize particular unstable periodic orbits associated with space-time patterns, or deliberately change the timescale of oscillatory patterns, and thus adjust and stabilize the frequency of the electronic device. Moreover, with a proper choice of feedback parameters one can also effectively control the coherence of spatio-temporal dynamics, e. g. enhance or destroy it. Increase of coherence is possible up to a reasonably large intensity of noise. However, as the level of noise grows, the efficiency of the control upon the temporal coherence decreases. 

The coefficients Oj are complicated expressions of the parameters of the system, and an exact evaluation of the Hopf condition is a very involved and tedious task. However, for the physically relevant regime of small inertia, i.e., r and Xy small, all the coefficients are positive if (10.23) is satisfied, and consequently (10.57) has no physically acceptable solution. The spatial Hopf bifurcation to oscillatory patterns cannot occur in hyperbolic reaction-diffusion systems with small inertia. 

Balasubramanian et al. in 1988 [75] reported first illustration of the inclusion of the BZ reaction into an AOT reverse micelle system. The coupling of an oscillating chemical reaction which shows spatial and temporal phenomenon relevant to biological systems was the main motivation for this study. In manganese-catalyzed reaction system oscillatory behavior was monitored for this particular case. Vanag et al. [76] has been studied the BZ-AOT reaction in a great detail emphasized in particular on the formation of non-equilibrium chemical patterns. 

In the previous chapters we predominantly considered catalysis as a molecular event, in which substrate molecules are activated by the catalyst. In this chapter and the next we will emphasize catalytic features of dimensions in space much larger than that of single catalytic centers and times much longer than those associated with the individual molecular catalytic cycles. Often mass and heat transport cause reaction cycles, which occur at different sites, to interact. Under particular conditions this gives rise to cooperative phenomena with oscillatory kinetics and temporal spatial organization. As such, interesting surface patterns such as spirals or pulsars may form. Such complex cooperative phenomena are known in physics as appearances of excitable systems. Their characteristic features are easily influenced by small variations in external conditions. Hence these systems have also features that are called adaptive. 

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