# Stabilizing synchrony by inhomogeneity

## TL;DR

Adding small differences in neuron firing rates can stabilize synchronized activity and improve spike timing precision in noisy environments.

## Contribution

The study reveals that inhomogeneity in neuronal oscillators can stabilize synchrony and increase spike train correlation under noise.

## Key findings

- Noise destroys isochronous synchrony in identical oscillators with positive phase resetting curves.
- Small inhomogeneity stabilizes phase locking and improves spike timing precision.
- Inhomogeneity increases correlation in synaptically connected neurons like the leaky integrate-fire model.

## Abstract

We show that for two weakly coupled identical neuronal oscillators with strictly positive phase resetting curve, isochronous synchrony can only be seen in the absence of noise and an arbitrarily weak noise can destroy entrainment and generate intermittent phase slips. Small inhomogeneity–mismatch in the intrinsic firing rate of the neurons–can stabilize the phase locking and lead to more precise relative spike timing of the two neurons. The results can explain how for a class of neuronal models, including leaky integrate-fire model, inhomogeneity can increase correlation of spike trains when the neurons are synaptically connected.