On the Approximation of Delayed Systems by Taylor Series Expansion

Research output: Article

15 Citations (Scopus)

Abstract

It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor series expansion of the delayed term approximates the asymptotic behavior of the original delayed system only for certain parameter regions, while for high-order expansions, the approximate system is unstable independently of the system parameters.

Original languageEnglish
Article number024503
JournalJournal of Computational and Nonlinear Dynamics
Volume10
Issue number2
DOIs
Publication statusPublished - márc. 1 2015

Fingerprint

Taylor Series Expansion
Taylor series
Approximation
Ordinary differential equations
Differential equations
Term
Delay Differential Equations
Ordinary differential equation
Asymptotic Behavior
Unstable
Scalar
Higher Order
Engineering

ASJC Scopus subject areas

  • Mechanical Engineering
  • Applied Mathematics
  • Control and Systems Engineering

Cite this

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AB - It is known that stability properties of delay-differential equations are not preserved by Taylor series expansion of the delayed term. Still, this technique is often used to approximate delayed systems by ordinary differential equations in different engineering and biological applications. In this brief, it is demonstrated through some simple second-order scalar systems that low-order Taylor series expansion of the delayed term approximates the asymptotic behavior of the original delayed system only for certain parameter regions, while for high-order expansions, the approximate system is unstable independently of the system parameters.

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