Role of disorder on the signal amplification in an array of unidirectionally coupled MEMS

In a recent work, it was shown that sinusoidal signals are amplified in an array of unidirectionnally
coupled MEMS and when the number of MEMS units was large enough, an instability leading to chaotic
behavior was observed [M.V. Tchakui et al., Eur. Phys. J. B 89, 22 (2016)]. In this work, we explore the
role of disorder in natural frequencies on the propagation and amplification of a signal in such an array.
Considering a random Gaussian distribution of natural frequencies, it is found that for small disorder
strength, the propagation takes place leading to oscillations in the array. Along the network, a decrease
of oscillations amplitude is observed in proportion as the disorder strength grows up. With large coupling
strength, the second transition to chaotic behavior is further postponed to a large MEMS rank up to its
disappearance as the disorder strength increases in a broaden frequency range. For very large disorder
strength the signal amplitude is damped to zero and there appears oscillations death.