title: Local and global synchronization transitions induced by time delays in small-world neuronal networks with chemical synapses.
abstract: Effects of time delay on the local and global synchronization in small-world neuronal networks with chemical synapses are investigated in this paper. Numerical results show that, for both excitatory and inhibitory coupling types, the information transmission delay can always induce synchronization transitions of spiking neurons in small-world networks. In particular, regions of in-phase and out-of-phase synchronization of connected neurons emerge intermittently as the synaptic delay increases. For excitatory coupling, all transitions to spiking synchronization occur approximately at integer multiples of the firing period of individual neurons; while for inhibitory coupling, these transitions appear at the odd multiples of the half of the firing period of neurons. More importantly, the local synchronization transition is more profound than the global synchronization transition, depending on the type of coupling synapse. For excitatory synapses, the local in-phase synchronization observed for some values of the delay also occur at a global scale; while for inhibitory ones, this synchronization, observed at the local scale, disappears at a global scale. Furthermore, the small-world structure can also affect the phase synchronization of neuronal networks. It is demonstrated that increasing the rewiring probability can always improve the global synchronization of neuronal activity, but has little effect on the local synchronization of neighboring neurons.
authors.affiliation: School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072 People's Republic of China.
authors.forename: Haitao
authors.initials: H
authors.lastname: Yu
authors.affiliation: School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072 People's Republic of China.
authors.forename: Jiang
authors.initials: J
authors.lastname: Wang
authors.affiliation: School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072 People's Republic of China.
authors.forename: Jiwei
authors.initials: J
authors.lastname: Du
authors.affiliation: School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072 People's Republic of China.
authors.forename: Bin
authors.initials: B
authors.lastname: Deng
authors.affiliation: School of Electrical Engineering and Automation, Tianjin University, Tianjin, 300072 People's Republic of China.
authors.forename: Xile
authors.initials: X
authors.lastname: Wei
keywords: Neuronal network; Small-world; Synchronization; Time delay