Nonlinear chemical reactions in dispersed media: The effect of slow mass exchange on the steady-state of the Schlögl models

The Schlögl-1 and bistable Schlögl-2 models in a spatially extended system are studied with the aid of a probabilistic cellular automaton (PCA) emulating chemical dynamics in a dispersed medium. Among the unusual effects observed are the significant deviation of the steady-state behavior from the deterministic value for Schlögl-1 model and two new bifurcations for Schlögl-2 model found under the conditions of intensive stirring and low rate constant kex of mass exchange between the adjacent cells of the PCA. One of these bifurcations results from the suppression of bi- and trimolecular reactions under the condition that the average number of particles 〈nX〉 in a cell is smaller than 1 and mass exchange rate is slow. The other bifurcation results from the competition between the mass exchange rate and the rate of autocatalysis in separate cells.