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

Oleg A. Bobrenkov, Morad Nazari, Eric 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 publicationProceedings of the ASME Design Engineering Technical Conference
Pages457-466
Number of pages10
Volume4
EditionPARTS A AND B
DOIs
StatePublished - 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

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

Fingerprint

Distributed Delay
Delay Differential Equations
MATLAB
Differential equations
Polynomials
Adaptive Meshing
Mathieu Equation
Periodic Coefficients
Monodromy
Chebyshev Polynomials
Chebyshev
Numerical integration
Continuous Time
Stability Analysis
Discretization
Computing
Approximation

ASJC Scopus subject areas

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

Cite this

Bobrenkov, O. A., Nazari, M., & Butcher, E. (2011). On the analysis of periodic delay differential equations with discontinuous distributed delays. In Proceedings of the ASME Design Engineering Technical Conference (PARTS A AND B ed., Vol. 4, pp. 457-466) https://doi.org/10.1115/DETC2011-47671

On the analysis of periodic delay differential equations with discontinuous distributed delays. / Bobrenkov, Oleg A.; Nazari, Morad; Butcher, Eric.

Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A AND B. ed. 2011. p. 457-466.

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

Bobrenkov, OA, Nazari, M & Butcher, E 2011, On the analysis of periodic delay differential equations with discontinuous distributed delays. in Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B edn, vol. 4, pp. 457-466, ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2011, Washington, DC, United States, 8/28/11. https://doi.org/10.1115/DETC2011-47671
Bobrenkov OA, Nazari M, Butcher E. On the analysis of periodic delay differential equations with discontinuous distributed delays. In Proceedings of the ASME Design Engineering Technical Conference. PARTS A AND B ed. Vol. 4. 2011. p. 457-466 https://doi.org/10.1115/DETC2011-47671
Bobrenkov, Oleg A. ; Nazari, Morad ; Butcher, Eric. / On the analysis of periodic delay differential equations with discontinuous distributed delays. Proceedings of the ASME Design Engineering Technical Conference. Vol. 4 PARTS A AND B. ed. 2011. pp. 457-466
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