  We have found two kinds of ultra-sensitive vibrational resonance in coupled
nonlinear systems. It is particularly worth pointing out that this
ultra-sensitive vibrational resonance is a transient behavior caused by
transient chaos. Considering long-term response, the system will transform from
transient chaos to periodic response. The pattern of vibrational resonance will
also transform from ultra-sensitive vibrational resonance to conventional
vibrational resonance. This article focuses on the transient ultra-sensitive
vibrational resonance phenomenon. It is induced by a small disturbance of the
high-frequency excitation and the initial simulation conditions, respectively.
The damping coefficient and the coupling strength are the key factors to induce
the ultra-sensitive vibrational resonance. By increasing these two parameters,
the vibrational resonance pattern can be transformed from an ultra-sensitive
vibrational resonance to a conventional vibrational resonance. The reason for
different vibrational resonance patterns to occur lies in the state of the
system response. The response usually presents transient chaotic behavior when
the ultra-sensitive vibrational resonance appears and the plot of the response
amplitude versus the controlled parameters shows a highly fractalized pattern.
When the response is periodic or doubly-periodic, it usually corresponds to the
conventional vibrational resonance. The ultra-sensitive vibrational resonance
not only occurs at the excitation frequency, but it also occurs at some more
nonlinear frequency components. The ultra-sensitive vibrational resonance as a
transient behavior and the transformation of vibrational resonance patterns are
new phenomena in coupled nonlinear systems.
