Stabilization of metastable dynamical rotating waves in a ring of unidirectionally coupled sigmoidal neurons due to shortcuts

Effects of shortcut connection on metastable dynamical rotating waves in a ring of sigmoidal neurons with unidirectional excitatory coupling are considered. A kinematical equation describing the propagation of wave fronts is derived with a sign function for the output function of neurons. Unstable rotating waves can be stabilized in the presence of an inhibitory shortcut. When a shortcut is excitatory and connects the most distant neurons, the dynamical metastability of rotating waves is lost. The duration of transient rotating waves then increases only linearly with the number of neurons, not exponentially. However, the dynamical metastability of rotating waves remains when a shortcut is local.