Vibrational Resonance in a Fractional Order Quintic Oscillator System with Time Delay Feedback

Abstract

Vibrational resonance is studied in a fractional order quintic oscillator system with delayed feedback. By utilizing the perturbation theory, the theoretical approximate expression of the response amplitude at low-frequency is obtained. In the presence of fractional order and time delay, resonance phenomena are studied in the single-well, double-well and triple-well potentials, respectively. Meanwhile, the good agreement between theoretical prediction and numerical simulation verifies the validity of theoretical analysis. It is found that by altering the fractional order derivative, the occurrence of new resonances is more frequent. As delay increases, the bifurcation point and the equilibrium point change periodically. In addition, fractional order, time delay feedback and high-frequency force amplitude can be appropriately selected to achieve the goal of maximizing the output in different systems. In particular, an intersection that affects the triple-well potential bifurcation point was found.