Ghost-vibrational resonance

• Resonance at a missing frequency of the input signal is achieved by a high-frequency force.
• For the Duffing system expression for response amplitude at the ghost-frequency is obtained.
• In a network, enhanced signal propagation occurs in the absence of high-frequency signal.
• Sigmoidal type of variation of response amplitude occurs with the unit number.

Ghost-stochastic resonance is a noise-induced resonance at a fundamental frequency missing in the input signal. We investigate the effect of a high-frequency, instead of a noise, in a single Duffing oscillator driven by a multi-frequency signal F(t)=∑i=1nficos(ωi+Δω0)t,ωi=(k+i-1)ω0, where k   is an integer greater than or equal to two. We show the occurrence of a high-frequency induced resonance at the missing fundamental frequency ω0ω0. For the case of the two-frequency input signal, we obtain an analytical expression for the amplitude of the periodic component with the missing frequency. We present the influence of the number of forces n, the parameter k  , the frequency ω0ω0 and the frequency shift Δω0Δω0 on the response amplitude at the frequency ω0ω0. We also investigate the signal propagation in a network of unidirectionally coupled Duffing oscillators. Finally, we show the enhanced signal propagation in the coupled oscillators in absence of a high-frequency periodic force.