Variety of Alternative Stable Phase-Locking in Networks of Electrically Coupled Relaxation Oscillators

We studied the dynamics of a large-scale model network comprised of oscillating electrically coupled neurons. Cells are modeled as relaxation oscillators with short duty cycle, so they can be considered either as models of pacemaker cells, spiking cells with fast regenerative and slow recovery variables or firing rate models of excitatory cells with synaptic depression or cellular adaptation. It was already shown that electrically coupled relaxation oscillators exhibit not only synchrony but also anti-phase behavior if electrical coupling is weak. We show that a much wider spectrum of spatiotemporal patterns of activity can emerge in a network of electrically coupled cells as a result of switching from synchrony, produced by short external signals of different spatial profiles. The variety of patterns increases with decreasing rate of neuronal firing (or duty cycle) and with decreasing strength of electrical coupling. We study also the effect of network topology--from all-to-all--to pure ring connectivity, where only the closest neighbors are coupled. We show that the ring topology promotes anti-phase behavior as compared to all-to-all coupling. It also gives rise to a hierarchical organization of activity: during each of the main phases of a given pattern cells fire in a particular sequence determined by the local connectivity. We have analyzed the behavior of the network using geometric phase plane methods and we give heuristic explanations of our findings. Our results show that complex spatiotemporal activity patterns can emerge due to the action of stochastic or sensory stimuli in neural networks without chemical synapses, where each cell is equally coupled to others via gap junctions. This suggests that in developing nervous systems where only electrical coupling is present such a mechanism can lead to the establishment of proto-networks generating premature multiphase oscillations whereas the subsequent emergence of chemical synapses would later stabilize generated patterns.