Ultradiscrete bifurcations for one dimensional dynamical systems

Shousuke Ohmori*, Yoshihiro Yamazaki

*この研究の対応する著者

研究成果: Article査読

1 被引用数 (Scopus)

抄録

Bifurcations of one dimensional dynamical systems are discussed based on some ultradiscrete equations. The ultradiscrete equations are derived from normal forms of one-dimensional nonlinear differential equations, each of which has saddle-node, transcritical, or supercritical pitchfork bifurcations. An additional bifurcation, which is similar to the flip bifurcation, is found in ultradiscrete equations for supercritical pitchfork bifurcations. 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 the FitzHugh-Nagumo model and discuss its dynamical properties.

本文言語English
論文番号122702
ジャーナルJournal of Mathematical Physics
61
12
DOI
出版ステータスPublished - 2020 12 1

ASJC Scopus subject areas

  • 統計物理学および非線形物理学
  • 数理物理学

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