Oscillation quenching induced by time-varying coupling functions

The oscillatory dynamics of natural and man-made systems can be disrupted by their time-varying interactions, leading to oscillation quenching phenomena in which the oscillations are suppressed. We introduce a framework for analyzing, assessing, and controlling oscillation quenching using coupling functions. Specifically, by observing limit-cycle oscillators, we investigate the bifurcations and dynamical transitions induced by time-varying diffusive and periodic coupling functions. We studied the transitions between oscillation quenching states induced by the time-varying form of the coupling function while the coupling strength is kept invariant. The time-varying periodic coupling function allowed us to identify novel, non-trivial inhomogeneous states that have not been reported previously. Furthermore, by using dynamical Bayesian inference, we have also developed a Proportional Integral controller that maintains the oscillations and prevents oscillation quenching from occurring. In addition to the present implementation and its generalizations, the framework carries broader implications for identification and control of oscillation quenching in a wide range of systems subjected to time-varying interactions.