Using a two-mode lumped model, we present theory and comprehensive bifurcation analysis of thermally coupled homogeneous-heterogeneous combustion of propane and methane in short monolith, fibermat or gauze type reactors with a focus on the dependence of the ignition, extinction, hysteresis, double and boundary limit loci on the various design and operating parameters. We analyze the impact of inlet fuel mole fraction, inlet temperature, residence time and channel hydraulic radius on the relative position of the homogeneous and catalytic ignition and extinction points and identify the parameter regions in which either catalytic or homogeneous reaction dominates. We also identify the regions in which catalytic ignition leads either to an intermediate branch on which the homogeneous reaction rate is negligible or directly to a high conversion and temperature state thereby facilitating homogeneous ignition. For the case of methane oxidation, we examine both the lean and rich feeds with the operating pressure as the bifurcation variable and compare the predicted results with available experimental data and numerical simulations using detailed CFD models. (C) 2015 Elsevier B.V. All rights reserved.