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This article investigates the emergence of phase synchronization in a networkof randomly connected neurons by chemical synapses. The study uses the classicHodgkin-Huxley model to simulate the neuronal dynamics under the action of atrain of Poissonian spikes. In such a scenario, we observed the emergence ofirregular spikes for a specific range of conductances, and also that the phasesynchronization of the neurons is reached when the external current is strongenough to induce spiking activity but without overcoming the coupling current.Conversely, if the external current assumes very high values, then an oppositeeffect is observed, i.e. the prevention of the network synchronization. Weexplain such behaviors considering different mechanisms involved in the system,such as incoherence, minimization of currents, and stochastic effects from thePoissonian spikes. Furthermore, we present some numerical simulations where thestimulation of only a fraction of neurons, for instance, can induce phasesynchronization in the non-stimulated fraction of the network, besides cases inwhich for larger coupling values it is possible to propagate the spikingactivity in the network when considering stimulation over only one neuron.

Phase synchronization in a sparse network of randomly connected neurons under the effect of Poissonian spike inputs