Beta-rhythm oscillations and synchronization transition in network models of Izhikevich neurons: effect of topology and synaptic type

TL;DR

This study investigates how network topology and synaptic types influence beta rhythm synchronization transitions in Izhikevich neuron models, revealing diverse behaviors including explosive and continuous transitions, with implications for understanding neuronal oscillations.

Contribution

It demonstrates the impact of synaptic interaction types and clustering coefficient on synchronization transitions, contrasting previous phase oscillator model findings.

Findings

Electrical synapses promote synchronization and explosive transitions.

Clustering coefficient determines transition order more than small-world properties.

Synchronization patterns shift from beta to gamma band due to refractory period changes.

Abstract

Despite their significant functional roles, beta-band oscillations are least understood. Synchronization in neuronal networks have attracted much attention in recent years with the main focus on transition type. Whether one obtains explosive transition or a continuous transition is an important feature of the neuronal network which can depend on network structure as well as synaptic types. In this study we consider the effect of synaptic interaction (electrical and chemical) as well as structural connectivity on synchronization transition in network models of Izhikevich neurons which spike regularly with beta rhythms. We find a wide range of behavior including continuous transition, explosive transition, as well as lack of global order. The stronger electrical synapses are more conducive to synchronization and can even lead to explosive synchronization. The key network element which determines the order of transition is found to be the clustering coefficient and not the small world effect, or the existence of hubs in a network. These results are in contrast to previous results which use phase oscillator models such as the Kuramoto model. Furthermore, we show that the patterns of synchronization changes when one goes to the gamma band. We attribute such a change to the change in the refractory period of Izhikevich neurons which changes significantly with frequency.