A uniformly distributed mathematical model (based on Semenov's theory of thermal explosions) is formulated to model the thermal behaviour of cellulosic materials in compost piles. The model consists of a mass balance equation for oxygen, a heat balance equation and incorporates the heat release due to biological activity within the pile. Singularity theory and degenerate Hopf bifurcation theory are used to investigate the generic properties of the model as well as to determine the loci of different singularities: the isola, cusp, double-limit points, boundary limit set, double-Hopf bifurcation, generalised Hopf (Bautin) bifurcation and Bogdanov-Takens bifurcation. These loci divide the secondary parameter plane into different regions of solution behaviours. Conditions under which biological activity can result in the initiation of an elevated-temperature branch within the compost pile which does not pose the risk of spontaneous ignition are identified. These are the ideal conditions for composting. The regions of parameter space when spontaneous ignition is likely are also determined. Crown Copyright (C) 2013 Published by Elsevier Ltd. All rights reserved.