Overcoming Oscillation Quenching via Mean-Field Feedback

Observational studies have shown that many natural systems need to remain in rhythmic oscillation activity. Yet, the appearance of oscillation quenching phenomena lead to the breakdown of intrinsic behavior of practical systems, often causing unpredictable results. To address the important problem about how to avoid or revive the paralyzed system, in this work, we use the mean-field function of the entire system as an external feedback acts on every unit. Taking the classical limit cycle of Stuart-Landau model as example, we find that oscillation quenching state can be eliminated effectively and thus revoke the deprived oscillation. Through extensive theoretical analyses and numerical simulations, the results show for various death scenarios that the oscillation quenching regions shrink drastically in the parameter space with increasing feedback strength. Our method can be regarded as a general framework to maintain or retrieve the continued oscillation for coupled nonlinear systems in diverse applications.