In this work, the TA3 thermoacoustic network is presented and used to simulate acoustic pulsations occurring in a heavy-duty ALSTOM gas turbine. In our approach, the combustion system is represented as a network of acoustic elements corresponding to hood, burners, flames and combustor. The multi-burner arrangement is modeled by describing the hood and combustor as Multiple Input Multiple Output (MIMO) acoustic elements. The MIMO transfer function (linking acoustic pressures and acoustic velocities at burner locations) is obtained by a three-dimensional modal analysis performed with a Finite Element Method. Burner and flame analytical models are fitted to transfer function measurements. In particular, the flame transfer function model is based on the time-lag concept, where the phase shift between heat release and acoustic pressure depends on the time necessary for the mixture fraction (formed at the injector location) to be convected to the flame. By using a state-space approach, the time domain solution of the acoustic field is obtained. The nonlinearity limiting the pulsation amplitude growth is provided by a fuel saturation term. Furthermore, Helmholtz dampers applied to the gas turbine combustor are acoustically modeled and included in the TA3 model. Finally, the predicted noise reduction is compared to that achieved in the engine.