The cycle-by-cycle variations in heat release are analyzed by means of a quasi-dimensional computer simulation and a turbulent combustion model. The influence of some basic combustion parameters with a clear physical meaning is investigated: the characteristic length of the unburned eddies entrained within the flame front, a characteristic turbulent speed, and the location of the ignition kernel. The evolution of the simulated time series with the fuel-air equivalence ratio, phi, from lean mixtures to over stoichiometric conditions, is examined and compared with previous experiments. Fluctuations on the characteristic length of unburned eddies are found to be essential to simulate the cycle-to-cycle heat release variations and recover experimental results. A non-linear analysis of the system is performed. It is remarkable that at equivalence ratios around phi similar or equal to 0.65, embedding and surrogate procedures show that the dimensionality of the system is small. (C) 2010 Elsevier Ltd. All rights reserved.