Center manifold reduction of periodic delay differential systems

Eric A. Butcher, Venkatesh Deshmukh, Ed Bueler

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

1 Scopus citations

Abstract

A technique for center manifold reduction of nonlinear delay differential equations (DDEs) with time-periodic coefficients is presented. Perturbation expansion converts the nonlinear response problem into solutions of a series of non-homogenous linear ordinary differential equations (ODEs) with time periodic coefficients. One set of linear non-homogenous ODEs is solved for each power of the perturbation parameter. Each ODE is solved by a Chebyshev spectral collocation method, Thus we compute a finite approximation to the nonlinear infinite-dimensional map for the DDE. Center manifold reduction on the map is then carried out. Center manifold reduction is illustrated via a single inverted pendulum including both a periodic retarded follower force and a nonlinear restoring force. In this example, the amplitude of the limit cycle associated with a flip bifurcation is found analytically and compared to that obtained from direct numerical simulation.

Original languageEnglish (US)
Title of host publication2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Pages711-719
Number of pages9
DOIs
StatePublished - Jun 17 2008
Externally publishedYes
Event6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007 - Las Vegas, NV, United States
Duration: Sep 4 2007Sep 7 2007

Publication series

Name2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007
Volume5 PART A

Other

Other6th International Conference on Multibody Systems, Nonlinear Dynamics and Control, presented at - 2007 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE2007
CountryUnited States
CityLas Vegas, NV
Period9/4/079/7/07

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Mechanical Engineering
  • Modeling and Simulation

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    Butcher, E. A., Deshmukh, V., & Bueler, E. (2008). Center manifold reduction of periodic delay differential systems. In 2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007 (pp. 711-719). (2007 Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2007; Vol. 5 PART A). https://doi.org/10.1115/DETC2007-34583