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Several integrate-to-threshold models with differing temporal integrationmechanisms have been proposed to describe the accumulation of sensory evidenceto a prescribed level prior to motor response in perceptual decision-makingtasks. An experiment and simulation studies have shown that the introduction oftime-varying perturbations during integration may distinguish among some ofthese models. Here, we present computer simulations and mathematical proofsthat provide more rigorous comparisons among one-dimensional stochasticdifferential equation models. Using two perturbation protocols and focusing onthe resulting changes in the means and standard deviations of decision times,we show that, for high signal-to-noise ratios, drift-diffusion models withconstant and time-varying drift rates can be distinguished fromOrnstein-Uhlenbeck processes, but not necessarily from each other. Theprotocols can also distinguish stable from unstable Ornstein-Uhlenbeckprocesses, and we show that a nonlinear integrator can be distinguished fromthese linear models by changes in standard deviations. The protocols can beimplemented in behavioral experiments.

Time-varying perturbations can distinguish among integrate-to-threshold models for perceptual decision-making in reaction time tasks