WIAS Preprint No. 1826, (2013)

Spectrum and amplitude equations for scalar delay-differential equations with large delay


  • Yanchuk, Serhiy
  • Lücken, Leonhard
  • Wolfrum, Matthias
    ORCID: 0000-0002-4278-2675
  • Mielke, Alexander
    ORCID: 0000-0002-4583-3888

2010 Mathematics Subject Classification

  • 34K08 35Q56


  • amplitude equations, delay-differential equations, large delay




The subject of the paper are scalar delay-differential equations with large delay. Firstly, we describe the asymptotic properties of the spectrum of linear equations. Using these properties, we classify possible types of destabilization of steady states. In the limit of large delay, this classification is similar to the one for parabolic partial differential equations. We present a derivation and error estimates for amplitude equations, which describe universally the local behavior of scalar delay-differential equations close to the destabilization threshold.

Appeared in

  • Discrete Contin. Dyn. Syst., 35 (2015) pp. 537--553.

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