Structural stochastic multiresonance in the Ising model on scale-free networks

Abstract

Stochastic resonance is investigated in the Ising model with ferromagnetic coupling on scale-free networks with various scaling exponents γ > 2 of the degree distributions p(k)∝k-γ, subjected to a weak oscillating magnetic field. The cases of networks constructed using the Configuration Model algorithm, with fully developed power-law tails of the degree distribution, and the Uncorrelated Configuration Model algorithm, with arbitrary constraint on the maximum connectivity of nodes, are considered. In the former case, for 2 < γ < 3 stochastic multiresonance is observed in the Monte Carlo simulations of the system, with the spectral power amplification exhibiting two or three maxima as a function of the temperature. Otherwise, the spectral power amplification has one maximum as a function of temperature and stochastic multiresonance does not occur. These results are in qualitative agreement with predictions of the linear response theory in the mean-field approximation, and quantitative differences between numerical and theoretical results can be mainly attributed to the disassortative character of the networks constructed using the Configuration Model algorithm.