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

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