Bursting hierarchy in an adaptive exponential integrate-and-fire network synchronization.

Neuronal network synchronization has received wide interest. In the present manuscript, we study the influence of initial membrane potentials together with network topology on bursting synchronization, in particular the sequential order of stabilized bursting among neurons. We find a hierarchical phenomenon on their bursting order. With a focus on situations where network coupling advances spiking times of neurons, we grade neurons into different layers. Together with the neuronal network structure, we construct directed graphs to indicate bursting propagation between different layers. More explicitly, neurons in upper layers burst earlier than those in lower layers. More interestingly, we find that among the same layer, bursting order of neurons is mainly associated with the number of neurons they connected to the upper layer; more stimuli lead to earlier bursting. Receiving effectively the same stimuli from the upper layer, we observe neurons with fewer connections would burst earlier.