Oscillation Quenching Induced By Time-Varying Coupling Functions

TL;DR

This paper presents a framework for analyzing and controlling oscillation quenching in systems with time-varying interactions, introducing new states and a Bayesian inference-based control method.

Contribution

It introduces a novel framework for analyzing, identifying, and controlling oscillation quenching caused by time-varying coupling functions in oscillatory systems.

Findings

Identified new inhomogeneous states induced by periodic coupling.

Developed a Bayesian inference method for system analysis.

Created a PI controller to prevent oscillation quenching.

Abstract

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 (PI) controller that maintains the oscillations and \red{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.