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Quasi-periodic Response Solution to Scalar State-Dependent Delay Differential Equation with Degenerate Equilibrium

  • Xiaolong He [1] ; Feng Jin [1] ; Yongli Song [1]
    1. [1] Hangzhou Normal University

      Hangzhou Normal University

      China

  • Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 5, 2024
  • Idioma: inglés
  • DOI: 10.1007/s12346-024-01104-x
  • Enlaces
  • Resumen

    • We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium.

      We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.

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