Revival of oscillations via weighted average feedback

Experimental studies have shown that many natural and artificial systems need to maintain stable oscillations during application, but the occurrence of oscillation quenching phenomenon will destroy the oscillation activity of the system and hinder the normal operation of the system. In this paper, to solve the important problem of oscillation quenching leading to system paralysis, the weighted average function of oscillators is applied to each oscillator as an external feedback, which is an extension of the mean-field feedback [N. Zhao and Z. Sun, Int. J. Bifurcation Chaos 30, 2050094 (2020)]. Taking the Stuart-Landau oscillators with the identical and nonidentical frequencies as examples, respectively, we find that the weighted average feedback is better than the previously proposed mean-field feedback in eliminating oscillation quenching with different coupling scenarios. Especially, when the weight is 0 or 1, that is, when a single oscillator is used as the feedback, the weighted average feedback is highly efficient in reviving oscillation. Our results provide a more convenient method to overcome these quenching states of coupled systems, and broaden the practical applications with respect to revoking rhythmic oscillations via external feedback in nature and real life.