We propose a simple, physically oriented model that explains important characteristics of cyclic combustion variations in spark-ignited engines. A key model feature is the interaction between stochastic, small-scale fluctuations in engine parameters and nonlinear deterministic coupling between successive engine cycles. Prior-cycle effects are produced by residual cylinder gas which alters volume-average in-cylinder equivalence ratio and subsequent combustion efficiency. The model's simplicity allows rapid simulation of thousands of engine cycles, permitting in-depth statistical studies of cyclic variation patterns. Additional mechanisms for stochastic and prior-cycle effects can be added to evaluate their impact on overall engine performance. We find good agreement with our experimental data.