Thermoacoustic oscillations occur in a Rijke burner with a porous plug stabilized premixed flame. In addition to regular limit cycle oscillations, the thermoacoustic system algb presents self-sustained periodic amplitude modulations, or beating oscillations, near the flame equivalence ratio limits of thermoacoustic instability. The beating oscillations exhibit approximately 1 Hz or even lower frequency amplitude modulations for the acoustic pressure and the heat release rate. It is also found that low frequency flame pulsations arise with the amplitude modulations. The different characteristics of the beating oscillations near the upper and lower equivalence ratio limits are distinguished and explained by the coupling between the low frequency flame pulsations and the thermoacoustic instability. To simulate the beating oscillations, this paper proposes a flame model that incorporates the flame dynamics at the amplitude modulation time scale (similar to s) and the acoustic time scale (similar to ms). The simulation results of the thermoacoustic system suggest that this flame model can qualitatively predict the amplitude modulation caused by the slow pulsating flame temperature and heat release rate. Flame heat loss plays an important role in low frequency flame pulsations, and its effects on beating oscillations are discussed. Several simulation cases at different equivalence ratios are performed to retrieve the amplitude modulations near the upper and lower equivalence ratio limits. The results are in keeping with the experimental observations. (C) 2016 The Combustion Institute. Published by Elsevier Inc. All rights reserved.