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We report novel theoretical results obtained from combining the method of largest Lyapunov exponent (LLE) with the spin-flip model (SFM), including noise, to model a vertical-cavity surface emitting laser (VCSEL) subject to polarized optical injection. The LLE is applied to the numerical solutions in order to automatically calculate stability maps that characterize the dynamics. The SFM has been extended and generalized to allow for optical injection of arbitrary polarization. Measurements on a 1550-nm VCSEL have been used to estimate the values of key parameters for use in the model and with these we demonstrate excellent agreement between theory and experiment.