The paper is devoted to the mathematical modeling of the dynamic behavior, which was observed experimentally during the study of methane oxidation over the two Pd foils coupled via the gas phase in a continuous stirred tank reactor (CSTR). The essential difference in the catalytic activity of the two identical Pd foils is simulated. Mathematical models, describing the reaction of methane oxidation over one Pd foil and over two identical pieces of the large foil divided in half are presented. At low oxygen pressure the symmetric steady state in the model for the two foils is stable and similar to that in the model of the single foil of a double area. With the inlet oxygen pressure increase the symmetric steady state becomes unstable via the pitch-fork bifurcation, and the two stable asymmetric states emerge. With a further oxygen pressure increase the state of one (active) foil approximately approaches the state of a single foil in the reactor with one foil, while the reaction rate on the other (passive) foil drastically decreases demonstrating that under some conditions only one foil can be active in a reactor with the two identical foils. The 'anti-phase' and the 'in-phase' oscillations of the reaction rate on two foils are also obtained in the simulations at low and high oxygen pressure in the agreement with the experimental observations. (C) 2016 Elsevier Ltd. All rights reserved.