An extended continuation problem for bifurcation analysis in the presence of constraints

Harry Dankowicz, Frank Schilder

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This paper presents an extended formulation of the basic continuation problem for implicitly-defined, embedded manifolds in ℝn. 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-co-dimension 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 package COCO and auxiliary toolboxes, including continuation of families of periodic orbits in a hybrid dynamical system with impacts and friction as well as detection and constrained continuation of selected degeneracies characteristic of such systems, such as grazing and switching-sliding bifurcations.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Pages311-321
Number of pages11
EditionPART A
DOIs
StatePublished - Jun 24 2010
Event2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009 - San Diego, CA, United States
Duration: Aug 30 2009Sep 2 2009

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
NumberPART A
Volume4

Other

Other2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009
Country/TerritoryUnited States
CitySan Diego, CA
Period8/30/099/2/09

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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