  We investigate the resonance behaviour in a system composed by n-coupled
Duffing oscillators where only the first oscillator is driven by a periodic
force, assuming a nearest neighbour coupling. We have derived the
frequency-response equations for a system composed of two-coupled oscillators
by using a theoretical approach. Interestingly, the frequency-response curve
displays two resonance peaks and one anti-resonance. A theoretical prediction
of the response amplitudes of two oscillators closely match with the
numerically computed amplitudes. We analyse the effect of the coupling strength
on the resonance and anti-resonance frequencies and the response amplitudes at
these frequencies. For the n-coupled oscillators system, in general, there are
n-resonant peaks and (n-1) anti-resonant peaks. For large values of n, except
for the first resonance, other resonant peaks are weak due to linear damping.
The resonance behaviours observed in the n-coupled Duffing oscillators are also
realized in an electronic analog circuit simulation of the equations.
Understanding the role of coupling and system size has the potential
applications in music, structural engineering, power systems, biological
networks, electrical and electronic systems.
