Mathematical model of traveling hybrid waves in a heterogeneous medium with chemical reactions in a gas phase and on a catalyst is considered. The coefficients of heat and mass transfer between the phases and the thermal conductivity of solid phase are determined from the current values of system parameters. We used methods of qualitative and quantitative analysis to study the behavior of phase trajectories of the dynamic system. We developed an efficient method of finding physically meaningful solution. We used simple kinetic equations to describe real chemical reactions and to solve a reverse problem of restoring mathematical model parameters. These results have important implications for characterization of structure of traveling hybrid waves. (C) 2014 The Combustion Institute. Published by Elsevier Inc. All rights reserved.