Stabilization of metastable dynamical rotating waves in a ring of unidirectionally coupled nonmonotonic neurons

Effects of nonmonotonicity in a sigmoidal output function of neurons on rotating waves in a ring of unidirectionally coupled neurons are studied. It is known that transient rotating waves show dynamical metastability when the output of neurons is monotonic; their duration increases exponentially with the number of neurons. Stable rotating waves of three types are generated as the nonmonotonicity in the output function of neurons increases. The type of stable rotating wave depends on whether the number of neurons is even or odd. Kinematical description for the propagation of wave fronts shows that an overshoot of the state of a neuron after the passage of the wave front due to the nonmonotonic output of a neuron causes the stabilization of rotating waves.