It is shown that a network of globally coupled integrate-and-fire neurons with pulse interaction possesses a variety of dynamical states with different patterns of synchronization. In the case of homogeneous external input, the network falls into the state of full synchrony in which all oscillators are phase-locked. In a network of excitatory neurons, this state is unstable to weak inhomogeneity: the system breaks into two subpopulations, one that is phase-locked and another that consists of aperiodic oscillators, the overall network activity being a periodic function of time. In the limit of vanishing inhomogeneity, the fraction of the unlocked population remains finite. Increasing the inhomogeneity quickly enters the network into the incoherent state. Adding a population of inhibitory neurons stabilizes the synchronization substantially and extends the dynamical variability of the system. Depending on the values of the parameters, the system can display periodic activity with several subpopulations, or synchronized aperiodic activity.
Pattern of Synchrony in Integrate-and-Fire-Networks
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