Burst synchronization of inhibitory spiking neuronal networks

Synchronized firing of spiking neuronal systems is considered to be crucial in the brain signal transmission and coding. In this paper, we incorporate a slow calcium ion channel into the classical Hodgkin-Huxley neuronal model and use it to construct spiking neuronal networks with heterogeneous neurons coupled by delayed chemical synapses, then explore the synchronized patterns of the networks in various conditions. First, synchronization for a two-neuron system is studied and it is found that neuronal systems with inhibitory synapses are more robust to variations of systematic parameters to achieve burst synchronization. Second, burst synchronization for a globally coupled neuronal network is investigated. It is interesting to find that although the single neuron emits spikes, the coupled neuronal network exhibits bursting behaviors with proper parameters. Furthermore, the robustness of the synchronization is sensitive to the parameter values of synaptic conductance and synaptic delay, but is less sensitive to the parameter values of synaptic decay time.