Effects of noise and variations on the duration of transient oscillations in unidirectionally coupled bistable ring networks.

We study effects of spatiotemporal noise and spatial variations on long-lasting transient oscillations in ring networks of unidirectionally coupled bistable elements (neurons), the duration of which increases exponentially with the number of neurons. On the one hand, spatiotemporal noise tends to sustain the transient oscillations. The duration of the oscillations occurring from fixed initial conditions changes nonmonotonically with noise strength and takes the maximum value at intermediate noise strength. Further, the duration of the oscillations is distributed in the form of the second power law and the mean duration increases with the number of neurons in the presence of an optimal noise. On the other hand, spatial variations degrade the exponential increases in the duration of the oscillations with the number of neurons. In the presence of fixed biases in the steady states of the neurons, there is a flat region in the distribution of the duration of the oscillations occurring under random initial conditions and an increase in the mean duration is almost linear with the number of neurons. Further, the duration of the oscillations in an ensemble of the networks with random biases drawing from an identical distribution is distributed in the form of the second power law and the ensemble mean increases in proportion to the five-halves power of the number of neurons.