Ultradiscrete bifurcations for one dimensional dynamical systems

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Abstract

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.

Original languageEnglish
Article number122702
JournalJournal of Mathematical Physics
Volume61
Issue number12
DOIs
Publication statusPublished - 2020 Dec 1

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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