Duration of transient oscillations in ring networks of unidirectionally coupled neurons

Properties of the duration of long lasting transient oscillations in ring networks of unidirectionally coupled sigmoidal neurons are derived with a kinematical model of traveling waves in the network. The duration of the transient oscillations occurring from random initial conditions increases exponentially as the number of neurons. The distribution of the duration is approximated by a power-law function when the number of neurons is large. Further, transient oscillations which oscillate about one thousand cycles before ceasing are observed in a network of forty neurons in circuit experiments though the duration decreases owing to random biases.