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  • Letter
  • Open Access

Phase and amplitude responses for delay equations using harmonic balance

R. Nicks*, R. Allen†, and S. Coombes‡

  • *Contact author: Rachel.Nicks@nottingham.ac.uk
  • †Contact author: pcyrga@exmail.nottingham.ac.uk
  • ‡Contact author: Stephen.Coombes@nottingham.ac.uk
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Phys. Rev. E 110, L012202 – Published 11 July, 2024

DOI: https://doi.org/10.1103/PhysRevE.110.L012202

Abstract

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a growing interest in the development of analogous approaches for DDEs to understand their response to external forcing. When combined with Floquet theory, the fundamental quantities for this reduction are phase and amplitude response functions. Here, we develop a framework for their construction that utilizes the method of harmonic balance.

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Information

Phys. Rev. E 110, L012202– Published 11 July, 2024
  • Received 26 April 2024
  • Accepted 28 June 2024
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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