A two-state discrete-time model is developed for the cycle-to-cycle dynamics in lean-fueled controlled autoignition engines. The main goal is to capture the cyclic variability in the combustion phasing which is a key performance variable in combustion control. The model is physics based, the states are the temperature and the fuel mass at intake valve closing, and simple enough so it may provide insights into the dynamics and causes of the behavior. The parameters are crudely calibrated using data that include late phasing approaching to misfire and the model captures the important effect of heat release during the re-compression of the residual gas. The model is shown to predict the coupling between cycles in the sense that, when driven by a stochastic input, the model reproduces the evolution and the magnitude of the cyclic variability with similar statistical properties to measured data.