An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints
An Extended Continuation Problem for Bifurcation Analysis in the Presence of Constraints
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DOI：
10.1115/1.4002684
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发表时间：
2011-07-01
影响因子：
2
通讯作者：
Schilder, Frank
中科院分区：
文献类型：
--
作者：
Dankowicz, Harry;Schilder, Frank
本文提出了 R(n) 中隐式定义的嵌入流形的基本连续问题的扩展表述。选择公式以便允许在连续过程中任意施加附加约束以及对相应的更高维解流形的选择性参数化的限制。特别是，形式主义被证明可以清楚地区分一方面面向应用程序的延续包中的核心例程所需的基本功能，另一方面由辅助工具箱提供的功能，这些辅助工具箱对延续问题的类和狭隘地关注特定问题实现的用户定义进行编码。选择了几个例子来说明形式主义及其在最近开发的延续核心包COCO和辅助工具箱中的实现，包括具有冲击和摩擦的混合动力系统中周期轨道族的延续，以及此类系统的选定简并特征的检测和约束延续，例如放牧和切换滑动分岔。 [DOI：10.1115/1.4002684]
This paper presents an extended formulation of the basic continuation problem for implicitly defined, embedded manifolds in R(n). The formulation is chosen so as to allow for the arbitrary imposition of additional constraints during continuation and the restriction to selective parametrizations of the corresponding higher-codimension solution manifolds. In particular, the formalism is demonstrated to clearly separate between the essential functionality required of core routines in application-oriented continuation packages, on the one hand, and the functionality provided by auxiliary toolboxes that encode classes of continuation problems and user definitions that narrowly focus on a particular problem implementation, on the other hand. Several examples are chosen to illustrate the formalism and its implementation in the recently developed continuation core package COCO and auxiliary toolboxes, including the continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as the detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations. [DOI: 10.1115/1.4002684]