Existence of Discrete Traveling Waves in Fully Coupled Network of Mackey–Glass Relay Generators

A fully coupled network of Mackey–Glass generators is considered. Each generator isdescribed by a limit equation for the Mackey–Glass equation. The right parts are represented by arelay function obtained when the exponent in the denominator of the nonlinearity tends to infinity.Discrete traveling waves are sought in the system. These modes are such that all components arerepresented by the same periodic function with successive (multiple of the same value) shifts.Moreover, this periodic function has the smallest number of switchings, that is, points at whichthe right-hand sides change the analytical form. It is shown that discrete traveling waves coexistin the system. Moreover, their number is equal to the factorial of the number of generators.