Vibrational resonance analysis in a fractional order Toda oscillator model with asymmetric potential

Abstract

This work is concerned with vibrational resonance (VR) in a fractional order Toda oscillator model with asymmetric potential. First, by virtue of the method of separation of slow and fast motions, we can directly obtain the approximate response amplitude at the low frequency. Then, considering the influence of the high-frequency signal and fractional order, the VR of such a system is investigated by theoretical analysis. It is worth noting that the fractional order has a significant effect on VR, which can be induced by changing the value of the fractional order. Moreover, for the Toda oscillator, establishing a fractional order model may be a new way to amplify weak low-frequency signals. In the end, some numerical simulations are worked out to illustrate the theoretical results.