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

TL;DR

This paper proves the existence of discrete traveling wave solutions in a fully coupled network of Mackey-Glass relay generators, revealing a factorial number of such modes based on the network size.

Contribution

It introduces a novel analysis of discrete traveling waves in Mackey-Glass relay networks and establishes their factorial multiplicity.

Findings

Discrete traveling waves coexist in the network.

Number of such waves equals factorial of the number of generators.

Traveling waves are characterized by minimal switchings in the relay functions.

Abstract

A fully coupled network of Mackey-Glass generators is considered. Each generator is described by a limit equation for the Mackey-Glass equation. The right parts are represented by a relay 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 are represented 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 which the right-hand sides change the analytical form. It is shown that discrete traveling waves coexist in the system. Moreover, their number is equal to the factorial of the number of generators.