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.

中文翻译：

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一维动力系统的超离散分岔

在一些超离散方程的基础上讨论了一维动力系统的分岔。超离散方程是从一维非线性微分方程的正规形式推导出来的，每个微分方程都有鞍点分岔、跨临界分岔或干草叉分岔。还讨论了类似于翻转分岔的附加分岔。这些超离散分岔的动力学特性可以通过图形分析来表征。作为我们处理应用的一个例子，我们关注 FitzHugh-Nagumo 模型的一个超离散方程，并讨论它的动力学特性。