Single or multiple synchronization transitions in scale-free neuronal networks with electrical or chemical coupling

Abstract In this paper, we have studied time delay- and coupling strength-induced synchronization transitions in scale-free modified Hodgkin–Huxley (MHH) neuron networks with gap-junctions and chemical synaptic coupling. It is shown that the synchronization transitions are much different for these two coupling types. For gap-junctions, the neurons exhibit a single synchronization transition with time delay and coupling strength, while for chemical synapses, there are multiple synchronization transitions with time delay, and the synchronization transition with coupling strength is dependent on the time delay lengths. For short delays we observe a single synchronization transition, whereas for long delays the neurons exhibit multiple synchronization transitions as the coupling strength is varied. These results show that gap junctions and chemical synapses have different impacts on the pattern formation and synchronization transitions of the scale-free MHH neuronal networks, and chemical synapses, compared to gap junctions, may play a dominant and more active function in the firing activity of the networks. These findings would be helpful for further understanding the roles of gap junctions and chemical synapses in the firing dynamics of neuronal networks.

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