Exponential transient propagating oscillations in a ring of spiking neurons with unidirectional slow inhibitory synaptic coupling

Transient oscillations in a ring of spiking neuron models unidirectionally coupled with slow inhibitory synapses are studied. There are stable spatially fixed steady firing–resting states and unstable symmetric propagating firing–resting states. In transients, firing–resting patterns rotate in the direction of coupling (propagating oscillations), the duration of which increases exponentially with the number of neurons (exponential transients). Further, the duration of randomly generated transient propagating oscillations is distributed in a power law form and spatiotemporal noise of intermediate strength sustains propagating oscillations. These properties agree with those of transient propagating waves in a ring of sigmoidal neuron models.

► We show exponential transient propagating oscillations in a ring of firing neuron models. ► We derive a kinematical description of the propagation of oscillations. ► We show that the duration of propagating oscillations increases exponentially with the number of neurons.