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To find an ignition and combustion control strategy in a gasoline-fueled HCCI engine equipped with the BlowDown SuperCharging (BDSC) system which is previously proposed by the authors, a one-dimensional HCCI engine cycle simulator capable of predicting the ignition and heat release of HCCI combustion was developed. The ignition and the combustion models based on Livengood-Wu integral and Wiebe function were implemented in the simulator. The predictive accuracy of the developed simulator in the combustion timing, combustion duration and heat release rate was validated by comparing to experimental results. Using the developed simulator, the control strategy for the engine operating mode switching between HCCI and SI combustion was explored with focus attention on transient behaviors of air-fuel ratio, A/F, and gas-fuel ratio, G/F.