System of monolith metallic (M) and ceramic (C) catalytic reactors described by two-phase model with axial dispersion is studied for CO oxidation. Values of kinetic and transport parameters are fitted to experimental ignition data. Periodic flow reversal is shown to stabilize temperature fronts in the C-M-C and M-C-M combination of monoliths. Existence of unsymmetric spatial temperature regimes and the possibility of adaptive control of flow direction switching are demonstrated.