Steady-state assumption, oscillatory

The empty-site requirement in Eq. (28) can be physically interpreted in one of two different ways either the adsorbed A and B have to rearrange prior to reaction, or they are bound to more than one adsorption site. For the latter case, the intermediate concentration is low, thus allowing a pseudo-steady-state assumption. Through the application of bifurcation analysis and catastrophe theory this model was found to predict a very rich bifurcation and dynamic behavior. For certain parameter values, sub- and supercritical Hopf bifurcations as well as homoclinic bifurcations were discovered with this simple model. The oscillation cycle predicted by such a model is sketched in Fig. 6c. This model was also used to analyze how white noise would affect the behavior of an oscillatory reaction system... 

The second assumption employed in this article is that all species designated as intermediates—those that do not enter into a given system as either terminal reactants or products—will be present at constant concentrations. This includes stationary systems that can be described by a unique steady state rather than those which exhibit transient or oscillatory behavior. 

One further note, the University of Delaware gasifier model used in the pseudo steady state approximation assumes that the gas and solids temperatures are the same within the reactor. That assumption removes an important dynamic feedback effect between the countercurrent flowing gas and solids streams. This is particularly important when the burning zone moves up and down within the reactor in an oscillatory manner in response to a step change in operating conditions. 

By the Poincare-Bendixson theorem, the system will have a periodic limit cycle solution when eq. (14.34) holds. This inequality defines a surface in the [CIO2]-[I2HMA] plane that separates the regions of stable oscillatory and steady states. The experimental range of oscillation is well described by this equation, except when the initial concentration of CIO2 is so low that it is nearly consumed in one oscillatory period, violating the assumption that (CIO2) is a constant. 

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