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A mathematical model, which simulates the complicated dynamic behavior experimentally observed during CO oxidation over Pd zeolite catalysts is presented. It describes the coupling of reaction rate oscillations, generated by various parts of the inhomogeneous catalytic layer through the gas phase. It can be shown, that the resulting dynamic behavior depends upon the difference between natural frequencies of local oscillators and the strength of coupling, which is defined mostly by the degree of conversion. Chaotic behavior could be identified under the condition of weak coupling for local oscillators with widely different natural frequencies. In the range of strong coupling the phenomenon of phase death has been obtained. A special type of intermittency chaos (“on–off” chaos) was observed in a small region of parameters under the conditions of strong coupling.

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A mesoscopic stochastic model of the catalytic reaction 2CO+O2→2CO2 on the surface of a metal particle is considered. The model is a Markovian chain of elementary reaction steps, which mimics the catalytic oxidation of CO on a nm-sized Pd particle. The model takes into account the effect of the particle size on the reaction rate and the role of temporal fluctuations of the concentrations of the reactants. The main goal of the paper is the comparison of the dynamics produced by the stochastic model and the deterministic model obtained via averaging of the master equation, while the catalyst particle size is reduced. Intrinsic fluctuations during the reaction are shown to change the reaction kinetics drastically for small metal particles with only several hundreds of surface atoms.

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Interesting kinetic phenomena, such as multiple steady states and kinetic oscillations recently found in the NOϩH 2 reaction over Rh͑533͒ and Rh͑111͒ single crystal surfaces in the 10 Ϫ6 mbar pressure range have been studied by means of experiments and computer modeling. A mathematical model, consisting of five ordinary differential equations and taking into account the lateral interactions in the adlayer, has been developed for simulating the NOϩH 2 /Rh͑533͒ and NOϩH 2 /Rh͑111͒ reactions. The simulation results make it possible to explain in detail the underlying reasons for the experimentally observed complex dynamic behavior. In particular, the kinetic oscillations and their properties have been reproduced. It was found that accumulation of NH ads species, which serves as an intermediate in the pathway of NH 3 production, is an important step in the oscillatory mechanism. In addition, the same mathematical model is able to successfully reproduce the experimental data concerning temperature programmed desorption ͑TPD͒ spectra, hysteresis phenomena, and the dependence of selectivity upon temperature and reactant partial pressures. Lateral interactions in the adlayer are shown to play a crucial role in the adequate simulation of the experimental observations.