  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
fraction of oscillators chosen randomly for coupling and forcing.
