Effects of time delay and non-Gaussian noise on the dynamics of a perceptual bistability

Abstract

In this paper, we investigate the effects of time delay and non-Gaussian noise on the dynamics properties of the attractor network model of perceptual bistability. Using delay Fokker–Planck equation and projection operator method, the stationary probability distribution Pst(x), the associated relaxation time Tc, and the normalized correlation function C(s) for perceptual bistability are obtained, respectively. Research results show that: (i) the time delay τ and the correlation time τ0 from non-Gaussian noise can induce the change of the peaks in the Pst(x), i.e., the transition of the system appears; (ii) there exhibits an optimal value of the τ0 or τ by which the Tc or C(s) is maximum, this maximum shows the τ0 or τ first reduces the stability of the attractor network model of perceptual bistability in the steady state, and then enhances it; and (iii) the noise intensity P or departure q from the Gaussian noise only enhances the stability of the attractor network model of perceptual bistability in the steady state.