Many perceptual and cognitive processes, like decision-making and bistable perception, involve multistable phenomena under the influence of noise. The role of noise in a multistable neurodynamical system can be formally treated within the Fokker-Planck framework. Nevertheless, because of the underlying nonlinearities, one usually considers numerical simulations of the stochastic differential equations describing the original system, which are time consuming. An alternative analytical approach involves the derivation of reduced deterministic differential equations for the moments of the distribution of the activity of the neuronal populations. The study of the reduced deterministic system avoids time consuming computations associated with the need to average over many trials. We apply this technique to describe multistable phenomena. We show that increasing the noise amplitude results in a shifting of the bifurcation structure of the system.