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We investigate lean-fueling cyclic dispersion in spark ignition engines in terms of experimental nonlinear mapping functions representing the connection between past and future combustion events. Nonlinear mapping functions provide a relatively easy method for identifying the deterministic dynamics associated with lean combustion instability, even in the presence of very high levels of noise. Observed experimental maps appear to have strong similarities to those predicted by an existing nonlinear spark ignition engine model. Differences between the observed map and model predictions become more pronounced at very lean fueling and high residual fraction. Map function details are shown to be useful in model validation, identifying model deficiencies, and comparing the characteristics of different engines. We expect that such maps will also be useful for developing real-time control strategies.