Within-burst synchrony changes for coupled elliptic bursters

TL;DR

This paper investigates a new phenomenon of within-burst synchrony changes in coupled elliptic bursters, revealing how higher order terms influence spike synchrony patterns during bursts.

Contribution

It introduces the concept of within-burst synchrony changes driven by higher order terms in the normal form of elliptic bursters.

Findings

Within-burst synchrony changes occur at turning points in spiking frequency.

Higher order terms can alter spike synchrony without affecting single burster behavior.

Synchronization patterns depend on coupling details and bifurcation structure.

Abstract

We study the appearance of a novel phenomenon for linearly coupled identical bursters: synchronized bursts where there are changes of spike synchrony within each burst. The examples we study are for normal form elliptic bursters where there is a periodic slow passage through a Bautin (codimension two degenerate Andronov-Hopf) bifurcation. This burster has a subcritical Andronov-Hopf bifurcation at the onset of repetitive spiking while end of burst occurs via a fold limit cycle bifurcation. We study synchronization behavior of two and three Bautin-type elliptic bursters for a linear direct coupling scheme. Burst synchronization is known to be prevalent behavior among such coupled bursters, while spike synchronization is more dependent on the details of the coupling. We note that higher order terms in the normal form that do not affect the behavior of a single burster can be responsible for changes in synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spiking frequency.