Desynchronizing two oscillators while stimulating and observing only one

TL;DR

This paper presents a method to desynchronize two coupled oscillators by stimulating only one, using phase-specific pulses and analyzing the system through phase response curves and time series data.

Contribution

It introduces a novel approach to desynchronize oscillators by stimulating a single unit and develops a rigorous theoretical framework based on phase approximation and response curves.

Findings

Desynchronization achieved by phase-specific stimulation of one oscillator.

Derived exact phase-isostable coordinate expressions for coupled oscillators.

Demonstrated how to infer phase response from time series data.

Abstract

Synchronization of two or more self-sustained oscillators is a well-known and studied phenomenon, appearing both in natural and designed systems. In some cases, the synchronized state is undesired, and the aim is to destroy synchrony by external intervention. In this paper, we focus on desynchronizing two self-sustained oscillators by short pulses delivered to the system in a phase-specific manner. We analyze a non-trivial case when we cannot access both oscillators but stimulate only one. The following restriction is that we can monitor only one unit, be it a stimulated or non-stimulated one. First, we use a system of two coupled Rayleigh oscillators to demonstrate how a loss of synchrony can be induced by stimulating a unit once per period at a specific phase and detected by observing consecutive inter-pulse durations. Next, we exploit the phase approximation to develop a rigorous theory formulating the problem in terms of a map. We derive exact expressions for the phase -- isostable coordinates of this coupled system and show a relation between the phase and isostable response curves to the phase response curve of the uncoupled oscillator. Finally, we demonstrate how to obtain phase response information from the system using time series and discuss the differences between observing the stimulated and unstimulated oscillator.