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The process of engine mapping in the automotive industry identifies steady-state engine responses by running an engine at a given operating point (speed and load) until its output has settled. While the time simulating this process with a computational model for one set of parameters is relatively short, the cumulative time to map all possible combinations becomes computationally inefficient. This work presents an alternative method for mapping out the steady-state response of an engine in simulation by applying bifurcation theory. The bifurcation approach used in this work allows the engine’s steady-state response to be traced through the model’s state-parameter space under the simultaneous variation of one or more model parameters. To demonstrate this approach, a bifurcation analysis of a simplified nonlinear engine model is presented.