# Suppression and Revival of Oscillations through Time-varying Interaction

## TL;DR

This paper investigates how time-varying coupling in oscillators can suppress and revive oscillations, revealing windows of stability and the effects of switching speed through bifurcation and stability analysis.

## Contribution

It introduces a model for switched coupling in oscillators and demonstrates how switching frequency and probability influence oscillation suppression and revival.

## Key findings

- Oscillations are suppressed within a specific coupling strength window.
- Faster switching leads to larger regions of oscillation suppression.
- The effective model accurately predicts stability regions and captures key dynamics.

## Abstract

We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We find, through bifurcation diagrams and Basin Stability analysis, that there exists a window in coupling strength where the oscillations get suppressed. Beyond this window, the oscillations are revived again. A similar trend emerges with respect to the relative predominance of the coupling forms, with the largest window of fixed point dynamics arising where there is balance in the probability of occurrence of the coupling forms. Further, significantly, more rapid switching of coupling forms yields large regions of oscillation suppression. Lastly, we propose an effective model for the dynamics arising from switched coupling forms and demonstrate how this model captures the basic features observed in numerical simulations and also offers an accurate estimate of the fixed point region through linear stability analysis.