论文标题
一维动力学系统的超差异分叉
Ultradiscrete Bifurcations for One Dimensional Dynamical Systems
论文作者
论文摘要
基于某些超级进程方程讨论了一维动力系统的分叉。超级进程方程源自一维非线性微分方程的正常形式，每个方程都有鞍形节点，跨临界或超临界干草叉分叉。在超临界干草叉分叉中发现了一个类似于翻转分叉的附加分叉。这些超级差异分叉的动力学特性可以通过图形分析来表征。作为我们治疗的应用的一个例子，我们专注于Fitzhugh-Nagumo模型的超差异方程，并讨论其动力学特性。
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 flip bifurcation, is found in ultradiscrete equations for supercritical pitchfork bifurcation. 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.
