On the global attractor of delay differential equations with unimodal feedback not satisfying the negative Schwarzian derivative condition

Daniel Franco, Chris Guiver, Hartmut Logemann, Juan Perán

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We study the size of the global attractor for a delay differential equation with unimodal feedback. We are interested in extending and complementing a dichotomy result by Liz and Röst, which assumed that the Schwarzian derivative of the nonlinear feedback is negative in a certain interval. Using recent stability results for difference equations, we obtain a stability dichotomy for the original delay differential equation in the situation wherein the Schwarzian derivative of the nonlinear term may change sign. We illustrate the applicability of our results with several examples.

Original languageEnglish
Article number76
Pages (from-to)1-15
Number of pages15
JournalElectronic Journal of Qualitative Theory of Differential Equations
Publication statusE-pub ahead of print - 21 Dec 2020


  • Delay differential equations
  • Difference equations
  • Global attractor

ASJC Scopus subject areas

  • Applied Mathematics

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