On the analysis of periodic delay differential equations with discontinuous distributed delays

Oleg A. Bobrenkov, Morad Nazari, Eric A. Butcher

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

Abstract

In this paper, the analysis of delay differential equations with periodic coefficients and discontinuous distributed delay is carried out through discretization by Chebyshev spectral continuous time approximation (ChSCTA). These features are introduced in the delayed Mathieu equation with discontinuous distributed delay used as an illustrative example. The efficiency of the process of stability analysis is improved by using shifted Chebyshev polynomials for computing the monodromy matrix, as well as the adaptive meshing of the parameter plane. An idea for a method for numerical integration of periodic DDEs with discontinuous distributed delay based on existing MATLAB functions is proposed.

Original languageEnglish (US)
Title of host publicationASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
Pages457-466
Number of pages10
EditionPARTS A AND B
DOIs
StatePublished - Dec 1 2011
Externally publishedYes
EventASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 - Washington, DC, United States
Duration: Aug 28 2011Aug 31 2011

Publication series

NameProceedings of the ASME Design Engineering Technical Conference
NumberPARTS A AND B
Volume4

Other

OtherASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011
CountryUnited States
CityWashington, DC
Period8/28/118/31/11

ASJC Scopus subject areas

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

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  • Cite this

    Bobrenkov, O. A., Nazari, M., & Butcher, E. A. (2011). On the analysis of periodic delay differential equations with discontinuous distributed delays. In ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011 (PARTS A AND B ed., pp. 457-466). (Proceedings of the ASME Design Engineering Technical Conference; Vol. 4, No. PARTS A AND B). https://doi.org/10.1115/DETC2011-47671