Catastrophe and propagation in chemical reactions

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Abstract
Multiple time scales, common in known chemical instability systems, lead to quasi-steady state ’’behavior’’ surfaces in the phase space of chemical concentrations. A result of catastrophe theory is used to classify the types of topological features, the ’’elementary catastrophes,’’ that these surfaces may take on. By using a multiple time scale scheme we predict the wave form and velocity of a variety of propagating phenomena that can occur because of the various types of catastrophes such as the cuspoids and umbilics. Since the state of chemical equilibrium is unique, we show that the presence of catastrophes on the behavior surface is strictly due to nonequilibrium processes on a short time scale. An important implication of this work is that the topological analysis of multiple time scale systems unfolds the richness of the potential for the variety of propagating phenomena in reacting diffusing systems.