Ultradiscrete Bifurcations for One Dimensional Dynamical Systems

Research output: Contribution to journalArticlepeer-review

Abstract

Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscretized equations. The ultradiscrete equations are derived from the normal forms of one-dimensional nonlinear differential equations, each of which has saddle-node, transcritical, or pitchfork bifurcations. An additional bifurcation, which is similar to flip bifurcation, is also discussed. Dynamical properties of these ultradiscrete bifurcations can be characterized with graphical analysis. As an example of application of our treatment, we focus on an ultradiscrete equation of FitzHugh-Nagumo model, and discuss its dynamical properties.

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2020 Apr 27

Keywords

  • Bifurcation
  • Discrete dynamical system
  • Normal forms
  • Ultradiscritization

ASJC Scopus subject areas

  • General

Fingerprint Dive into the research topics of 'Ultradiscrete Bifurcations for One Dimensional Dynamical Systems'. Together they form a unique fingerprint.

Cite this