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Yang, Tao; Liu, Ruifen; Zeng, Chunhua; Duan, Weilong

Effects of time delay and non-Gaussian noise on the dynamics of a perceptual bistability. (English) Zbl 1539.60077

Chin. J. Phys., Taipei 55, No. 2, 275-288 (2017).
Summary: 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 \(P_{st}(x)\), the associated relaxation time \(T_c\), and the normalized correlation function \(C(s)\) for perceptual bistability are obtained, respectively. Research results show that: (i) the time delay \(\tau\) and the correlation time \(\tau_0\) from non-Gaussian noise can induce the change of the peaks in the \(P_{st}(x)\), i.e., the transition of the system appears; (ii) there exhibits an optimal value of the \(\tau_0\) or \(\tau\) by which the \(T_c\) or \(C(s)\) is maximum, this maximum shows the \(\tau_0\) or \(\tau\) 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.

Cited in 3 Documents

MSC:

60H15 Stochastic partial differential equations (aspects of stochastic analysis)
60H40 White noise theory
82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics
35Q84 Fokker-Planck equations
93E15 Stochastic stability in control theory

Keywords:

associated relaxation time; normalized correlation function; time delay; perception bistability
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