Synchronization of oscillators coupled through an environment

TL;DR

This paper analyzes how oscillators indirectly synchronize through an environment, providing stability criteria and demonstrating that weak coupling can induce synchronization if appropriately signed, with applications to biological neuron models.

Contribution

It establishes general criteria for the stability of synchronized oscillations via environmental coupling and proves weak coupling can synchronize oscillators with the correct sign.

Findings

Weak environmental coupling can synchronize oscillators if of the right sign.

Derived stability criteria for synchronized oscillations.

Applied results to biological neuron models and lambda-omega oscillators.

Abstract

We study synchronization of oscillators that are indirectly coupled through their interaction with an environment. We give criteria for the stability or instability of a synchronized oscillation. Using these criteria we investigate synchronization of systems of oscillators which are weakly coupled, in the sense that the influence of the oscillators on the environment is weak. We prove that arbitrarily weak coupling will synchronize the oscillators, provided that this coupling is of the 'right' sign. We illustrate our general results by applications to a model of coupled GnRH neuron oscillators proposed by Khadra and Li, and to indirectly weakly-coupled lambda-omega oscillators