Exponential dispersion relation and its effects on unstable propagating pulses in unidirectionally coupled symmetric bistable elements

The propagation of pulses in unidirectionally coupled symmetric bistable elements is studied. The speeds of unstable traveling pulse waves in a ring of elements increase with pulse width in an exponential manner. This dispersion relation causes exponential increases in the duration of transient propagating pulses and the noise-sustained propagation of pulses, which are qualitatively the same as those in a reaction–diffusion–convection equation and a ring of sigmoidal neurons. However, the speeds of pulse fronts in propagating pulses depend on the backward pulse width. Properties of pulse transmission in an open chain of elements then differ from those in the above two systems qualitatively.