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We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piecewise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients.

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Explicit Periodic Solutions in a Delay Differential Equation

  • 会议论文

  • 发表日期：

    2025年

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  • Anatoli Ivanov,
  • Sergiy Shelyag

摘要

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known idea of reduction to interval maps is used in the case under consideration, when both the defining nonlinearity and the periodic coefficient are piecewise constant functions. The stable periodic dynamics persist under a smoothing procedure in a small neighborhood of the discontinuity set. This work continues the research in recent paper [7] on stable periodic solutions of differential delay equations with periodic coefficients.