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In order to further understand phenomena observed during studies of adiabatic excitation of longitudinal bunch shape oscillations [M. Bai et al., Phys. Rev. ST Accel. Beams 3, 064001 (2000)], we have developed a simulation using a one-turn map. In this report we will present the physical foundations for the simulation and the methods used in the simulator. We will present simulation results using parameters of actual experiments, along with the corresponding experimental results.