Ghost-Stochastic Resonance in a Unidirectionally Coupled and Small-World Networks

Abstract

Ghost-stochastic resonance is a noise-induced resonance at a missing fundamental frequency in the input signal. In this paper we investigate the features of ghost-stochastic resonance in a unidirectionally coupled network and small-world network with each unit being bistable Bellows map. In the one-way coupled network we apply a multi-frequency signal $(1/n_{\mathrm{f}}) \sum_{j=1}^{n_{\mathrm{f}}} \cos (\omega_{j}n)$, $n=0,1,2,\cdots$, $\omega_{j}=(k+j-1)\omega_{0}$, with $k$ being an integer $\ge2$ (without the fundamental frequency $\omega_{0}$) and noise to first unit only. We show the occurrence of resonance and undamped signal propagation for coupling strength above a certain critical value. The response amplitude shows sigmoidal function type variation with unit number. We report the effect of coupling strength $\delta$, $k$ and $n_{\mathrm{f}}$ on the response amplitude. In the small-world network randomness in the connectivity topology is described by the probability $p$ of rewiring of units in a ring type regular network where all the units are subjected to noise and multi-frequency signal. We present the influence of $p$ and the coupling strength on the probability distribution of response amplitude $Q$ of various units, $\langle Q \rangle$ and the maximum value of $Q$.