Within-Burst Synchrony Changes for Coupled Elliptic Bursters

Abstract

We study a novel phenomenon for 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 around a Bautin (codimension two degenerate Andronov–Hopf) bifurcation. This burster has a subcritical Andronov–Hopf bifurcation at the onset of repetitive spiking, while the 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 as well as demonstrating the phenomenon in an approximation of gap-junction and synaptic coupling. Burst synchronization is known to be prevalent 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 the synchrony pattern; more precisely, we find within-burst synchrony changes associated with a turning point in the spiking frequency.