title: Effect of multiple time-delay on vibrational resonance.
abstract: We report our investigation on the effect of multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a low- and a high-frequency periodic force. For the single oscillator, we obtain analytical expressions for the response amplitude Q and the amplitude g of the high-frequency force at which resonance occurs. The regions in parameter space of enhanced Q at resonance, as compared to the case in absence of time-delay, show a bands-like structure. For the two-coupled oscillators, we explain all the features of variation of Q with the control parameter g. For the system of n-coupled oscillators with a single time-delay coupling, the response amplitudes of the oscillators are shown to be independent of the time-delay. In the case of a multi time-delayed coupling, undamped signal propagation takes place for coupling strength (δ) above a certain critical value (denoted as δu). Moreover, the response amplitude approaches a limiting value QL with the oscillator number i. We obtain analytical expressions for both δu and QL.
authors.affiliation: School of Physics, Bharathidasan University, Tiruchirappalli 620 024, Tamil Nadu, India. c.jeeva1987@gmail.com
authors.forename: C
authors.initials: C
authors.lastname: Jeevarathinam
authors.forename: S
authors.initials: S
authors.lastname: Rajasekar
authors.forename: M A F
authors.initials: MA
authors.lastname: Sanjuán
mesh_terms: D003198:Computer Simulation; D004867:Equipment Design; D005246:Feedback; D017711:Nonlinear Dynamics; D009716:Numerical Analysis, Computer-Assisted; D009991:Oscillometry / Q000295:instrumentation; D010507:Periodicity; D013997:Time Factors; D014732:Vibration