论文标题
具有延迟的系统的分叉分析：方法及其在应用中的使用
Bifurcation Analysis of Systems with Delays: Methods and Their Use in Applications
论文作者
论文摘要
本章介绍了有延迟系统研究的动态系统的观点。重点是如何将分叉理论的高级工具（例如在软件包dde-biftool中实现）应用于应用在应用中产生的延迟微分方程（DDE）的研究，包括那些具有状态依赖性延迟的应用程序。我们讨论了DDE-Biftool最新版本的当前功能。它们包括稳态的数值延续，周期性的轨道及其分叉的旋转，以及检测二拟合二的某些分叉以及其正常形式的计算。 El Nino现象的概念DDE模型和具有两个依赖状态依赖性反馈术语的概念DDE模型的两个较长案例研究，证明可以以这种方式获得哪种见解。
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of delay differential equations (DDEs) arising in applications, including those that feature state-dependent delays. We discuss the present capabilities of the most recent release of DDE-BIFTOOL. They include the numerical continuation of steady states, periodic orbits and their bifurcations of codimension one, as well as the detection of certain bifurcations of codimension two and the calculation of their normal forms. Two longer case studies, of a conceptual DDE model for the El Nino phenomenon and of a prototypical scalar DDE with two state-dependent feedback terms, demonstrate what kind of insights can be obtained in this way.
