Emergence of spiking activity in a network of synaptically coupled neurons with axonal delays

Oscillatory spiking activity of neuronal networks as possible mechanism of information representation and encoding is a subject of intensive discussions in experimental and mathematical neuroscience. Self-sustained network spiking patterns may appear due to the presence of local oscillatory cells (pacemakers) continuously stimulating their neighbors through the synaptic couplings. Alternatively, the patterns may be induced by a constant external drive (rhythmic or noisy signals) providing sequential excitations of the network cells. We consider the network of originally non-oscillatory neurons and analyze the possibility of spontaneous spiking due to cycling excitations along closed routes or loops. As a biological background we use experimental data of neuronal culture activity recorded by multielectrode array (MEA) technology. As a mathematical model we construct a network of synaptically coupled Hodgkin-Huxley neurons with relatively small number of cells interacting by full graph topology of synaptic excitatory/inhibitory couplings. We show that there is a critical coupling strength above which the network starts to generate self-sustained spiking patterns. Using a cross-correlation analysis of model data we identify simple local excitation routes in the form of correlated spiking events.