Title: Ghost stochastic resonance in an asymmetric Duffing oscillator

Abstract

Nonlinear systems excited by noise and periodic forces composed of several frequencies exhibit the phenomenon of ghost stochastic resonance, which is found in several scientific fields ranging from biology to geophysics. The common novelty is the emergence at the output of the system of a frequency called "ghost frequency" that is absent at the input. The discovery of the existence of this phenomenon has led to the understanding of a whole range of problems, from the perception of the pitch of complex sounds or visual stimuli, to the explanation of climate cycles. In this study, we report the occurrence of the ghost stochastic resonance (GSR) for a Brownian particle in three types of asymmetry potentials. The dynamics of the particle is described by a Duffing oscillator. The asymmetries are controlled by the asymmetry parameter and introduced into the potential by varying the left well. These variations are: depth only, width only and both depth and width. The properties of the GSR in asymmetric systems are different from those of the symmetric system. It is shown that the observed resonance at the ghost frequency is due to the existence of this frequency during the dynamics of the particle. We also examine numerically the effect of the asymmetry parameter on the GSR phenomenon. It is found that the asymmetry parameter has a significant influence on the GSR and allows a precise control of the GSR occurrence.