On the Weak Signal Amplification by Twice Sampling Vibrational Resonance Method in Fractional Duffing Oscillators

Abstract

In our former work developed by Yang et al. (2017, “Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators,” ASME J. Comput. Nonlinear Dyn., 12(5), p. 051011), we put forward the rescaled vibrational resonance (VR) method in fractional duffing oscillators to amplify a weak signal with arbitrary high frequency. In the present work, we propose another method named as twice sampling VR to achieve the same goal. Although physical processes of two discussed methods are different, the results obtained by them are identical completely. Besides the two external signals excitation case, the validity of the new proposed method is also verified in the system that is excited by an amplitude modulated signal. Further, the dynamics of the system reveals that the resonance performance, i.e., the strength and the pattern, depends on the fractional order closely.