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Synchronization is an important collective phenomenon in interactingoscillatory agents. Many functional features of the brain are related tosynchronization of neurons. The type of synchronization transition that mayoccur (explosive vs. continuous) has been the focus of intense attention inrecent years, mostly in the context of phase oscillator models for whichcollective behavior is independent of the mean-value of natural frequency.However, synchronization properties of biologically-motivated neural modelsdepend on the firing frequencies. In this study we report a systematic study ofgamma-band synchronization in spiking Hodgkin-Huxley neurons which interact viaelectrical or chemical synapses. We use various network models in order todefine the connectivity matrix. We find that the underlying mechanisms andtypes of synchronization transitions in gamma-band differs from beta-band. Ingamma-band, network regularity suppresses transition while randomness promotesa continuous transition. Heterogeneity in the underlying topology does not leadto any change in the order of transition, however, correlation between numberof synapses and frequency of a neuron will lead to explosive synchronization inheterogenous networks with electrical synapses. Furthermore, small-worldnetworks modeling a fine balance between clustering and randomness (as in thecortex), lead to explosive synchronization with electrical synapses, but asmooth transition in the case of chemical synapses. We also find thathierarchical modular networks, such as the connectome, lead to frustratedtransitions. We explain our results based on various properties of the network,paying particular attention to the competition between clustering andlong-range synapses.

physica d nonlinear phenomena

Explosive, continuous and frustrated synchronization transition in  spiking Hodgkin-Huxley neuronal networks: the role of topology and synaptic  interaction