Ultrasensitive vibrational resonance induced by small disturbances

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.