English

A simple model for ultradiscrete Hopf bifurcation

Chaotic Dynamics 2021-04-01 v1 Mathematical Physics math.MP

Abstract

Dynamical properties of ultradiscrete Hopf bifurcation, similar to those of the standard Hopf bifurcation, are discussed by proposing a simple model of ultradiscrete equations with max-plus algebra. In ultradiscrete Hopf bifurcation, limit cycles emerge depending on the value of a bifurcation parameter in the model. The limit cycles are composed of a finite number of discrete states. Furthermore, the model exhibits excitability. The model is derived from two different dynamical models with Hopf bifurcation by means of ultradiscretization; it is a candidate for a normal form for ultradiscrete Hopf bifurcation.

Keywords

Cite

@article{arxiv.2103.16777,
  title  = {A simple model for ultradiscrete Hopf bifurcation},
  author = {Shousuke Ohmori and Yoshihiro Yamazaki},
  journal= {arXiv preprint arXiv:2103.16777},
  year   = {2021}
}
R2 v1 2026-06-24T00:43:04.466Z