Stochastic resonance in the majority vote model on regular and small-world lattices

Abstract

The majority vote model with two states on regular and small-world networks is considered under the influence of periodic driving. Monte Carlo simulations show that the time-dependent magnetization, playing the role of the output signal, exhibits maximum periodicity at nonzero values of the internal noise parameter [Formula: see text], which is manifested as the occurrence of the maximum of the spectral power amplification; the location of the maximum depends in a nontrivial way on the amplitude and frequency of the periodic driving as well as on the network topology. This indicates the appearance of stochastic resonance in the system as a function of the intensity of the internal noise. Besides, for low frequencies and for certain narrow ranges of the amplitudes of the periodic driving double maxima of the spectral power amplification as a function of [Formula: see text] occur, i.e., stochastic multiresonance appears. The above-mentioned results quantitatively agree with those obtained from numerical simulations of the mean-field equations for the time-dependent magnetization. In contrast, analytic solutions for the spectral power amplification obtained from the latter equations using the linear response approximation deviate significanlty from the numerical results since the effect of the periodic driving on the system is not small even for vanishing amplitude.