A numerical approach based on dynamic importance sampling (DIMS) is introduced to investigate the activation problem in two-dimensional nonequilibrium systems. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. A shift in the position of the escape path compared to a heteroclinic trajectory calculated in the limit of zero noise intensity is directly observed. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.
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