Periodicity of limit cycles in a max-plus dynamical system

TL;DR

This paper investigates the periodic behavior of a max-plus dynamical system, analyzing the number of states in its limit cycles and the conditions under which quasi-periodic cycles occur, with approximate relations based on bifurcation parameters.

Contribution

It introduces a max-plus dynamical system with limit cycles and explores their periodicity, including the existence of quasi-periodic cycles and relations to bifurcation parameters.

Findings

Limit cycles have a discrete number of states.

Quasi-periodic cycles depend on bifurcation parameters.

Approximate relations link cycle states to bifurcation values.

Abstract

By introducing a max-plus dynamical system having limit cycles, we discuss their periodicity, especially the number of discrete states in them. We also find that quasi-periodic cycles exist depending on the bifurcation parameter in the system. Approximate relations between the number of states in the limit cycles and the value of the bifurcation parameter are proposed.