Ghost Resonances

Abstract

As shown in Sect. 2.2, when a bistable or an excitable system is driven by a periodic force of frequency, say, f and subjected to a weak noise it exhibits the phenomenon of stochastic resonance at an optimum noise level. Essentially, the signal-to-noise ratio (SNR) measured at the frequency f of the driving periodic force becomes maximum at a value of the noise intensity. At resonance, in the bistable system almost a periodic switching between the two coexisting states or potential wells occurs, with frequency 2f or period 1∕(2f). That is, the mean residence time about a coexisting state or a potential well is 1∕(2f). In excitable systems at resonance, the mean time duration (also called waiting time) between two consecutive bursts/pulses is 1∕(2f) or the mean frequency of bursts is 2f. Note that in the noise-induced stochastic resonance phenomenon the system is driven by a single periodic force. The study of the response of a system to external signals comprising the number of periodic forces of different frequencies is of great important in understanding the response and functioning of many physical and biological systems. For example, signals such as musical tones and human speech received by sensory neurons often contain numerous discrete spectral lines.