Signal amplification by unidirectional coupling of oscillators

We report our investigation on the input signal amplification in unidirectionally coupled monostable Duffing oscillators in one- and two dimensions with first oscillator alone driven by a weak periodic signal. Applying a perturbation theory, we obtain a set of nonlinear equations for the response amplitude of the coupled oscillators. We identify the conditions for undamped signal propagation with enhanced amplitude through the coupled oscillators. When the number of oscillators increases the response amplitude approaches a limiting value. We determine this limiting value. Also, we analyse the signal amplification in the coupled oscillators in two dimensions with a fraction of oscillators chosen randomly for coupling and forcing.