论文标题
Bogdanov-Takens分叉在延迟微分方程中的分叉分析
Bifurcation analysis of Bogdanov-Takens bifurcations in delay differential equations
论文作者
论文摘要
在本文中，我们将在经典延迟微分方程（DDES）中进行通用和跨临界的codimension两次bogdanov-takens分叉附近的参数依赖性中心歧管还原。使用Lindstedt-Poincaré方法的概括来近似于同型解决方案，使我们能够初始化从这些点散发出的同型分叉曲线的延续。正常形式的转化是在使用基于弗雷德霍尔姆替代方案的归一化技术的双重半群（Sun-Star conculus）的功能分析扰动框架中得出的。获得的表达式提供了明确的公式，这些公式已在免费提供的分叉软件包DDE-Biftool中实现。各种模型都证明了有效性。
In this paper, we will perform the parameter-dependent center manifold reduction near the generic and transcritical codimension two Bogdanov-Takens bifurcation in classical delay differential equations (DDEs). Using a generalization of the Lindstedt-Poincaré method to approximate the homoclinic solution allows us to initialize the continuation of the homoclinic bifurcation curves emanating from these points. The normal form transformation is derived in the functional analytic perturbation framework for dual semigroups (sun-star calculus) using a normalization technique based on the Fredholm alternative. The obtained expressions give explicit formulas, which have been implemented in the freely available bifurcation software package DDE-BifTool. The effectiveness is demonstrated on various models.
