Variation of Response Amplitude in Parametrically Driven Single Duffing Oscillator and Unidirectionally Coupled Duffing Oscillators - Rajamani, S.; Rajasekar, S. (Journal of Applied Nonlinear Dynamics, 2026)
We present our investigation on the effect of parametric force on the response amplitude in the single Duffing oscillator and unidirectionally coupled n Duffing oscillators. In the single oscillator parametric perturbation is of the form f xsinωt. Parametric perturbation induced oscillatory motion is found for values of f above a critical value. In the oscillatory motion the dominant frequency is found to be ω/2. A(ω/2), the amplitude of oscillation at the frequency ω/2, is found to vary linearly with ω. We consider unidirectionally coupled n oscillators with first oscillator alone driven by a parametric force and the other oscillators are nonlinearly or linearly coupled but one-way only. Depending upon the values of the coupling strength δ the oscillators, after first several oscillators, exhibit damped or undamped signal propagation. In the nonlinearly coupled oscillators the dominant frequency of oscillation is ω/2. In the linearly coupled system the frequency ω/2 is absent. The oscillators other than the first oscillator exhibiting oscillatory motions have frequencies ω or 2ω or both depending upon the values of the coupling strength.