Parameter identification in periodic delay differential equations with distributed delay

Shahab Torkamani, Eric A. Butcher, Firas A. Khasawneh

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

In this study, a parameter identification approach for identifying the parameters of a periodic delayed system with distributed delay is introduced based on time series analysis and spectral element analysis. Using this approach the parameters of the distributed delayed system can be identified from the time series of the response of the system. The experimental or numerical data of the response is examined with Floquet theory and time series analysis techniques to estimate a reduced order dynamics, or truncated state space to identify the Floquet multipliers. Parameter identification is then completed using a dynamic map developed for the assumed model of the system which can relate the Floquet multipliers to the unknown parameters in the model. The parameter identification technique is validated numerically for first and second order delay differential equations with distributed delay.

Original languageEnglish (US)
Pages (from-to)1016-1026
Number of pages11
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume18
Issue number4
DOIs
StatePublished - Apr 2013

Keywords

  • Delay system
  • Distributed delay
  • Integro-differential equations
  • Parameter identification

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Applied Mathematics

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