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.
Highlights
Synchronization is an important collective phenomenon that may emerge in locally interacting physical and biological oscillatory systems (Pikovsky et al, 2001; Barahona and Pecora, 2002; Motter et al, 2005; Arenas et al, 2008)
Our main results are as follows: (i) we find that electrical synapses are more conducive to synchronization than chemical synapses, leading to explosive synchronization in beta band in random networks. (ii) we find that the effect of clustering is far more important than small-world effect in determining the order of transition. (iii) we find that patterns of synchronization are distinctly different in beta band from the corresponding transitions in the high frequency gamma band
We found that stronger electrical synapses are more conducive to synchronize than chemical synapses, regardless of network structure
Summary
Synchronization is an important collective phenomenon that may emerge in locally interacting physical and biological oscillatory systems (Pikovsky et al, 2001; Barahona and Pecora, 2002; Motter et al, 2005; Arenas et al, 2008). Neural tissue of central nervous system can generate oscillatory activity in various scales from individual neuron firing to macroscopic oscillations in large neural ensembles (Engel et al, 2001; Varela et al, 2001; Buzsaki and Draguhn, 2004; Jensen and Lisman, 2005; Buzsaki, 2006). Neural oscillations have been documented to cover a broad spectrum of frequencies These oscillations are observed widely in every level of central nervous system and are usually categorized into five frequency bands: delta 0.5 − 3.5 Hz, theta 4 − 7 Hz, alpha 8 − 12 Hz, beta 13 − 30 Hz, and gamma > 30 Hz (Buzsaki, 2006; Rosanova et al, 2009). Beta waves are associated with the activities of motor cortex (Baker, 2007; Engel and Fries, 2010)
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