Phase and amplitude responses for delay equations using harmonic balance
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866910424652316672 |
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| author | Nicks, Rachel Allen, Robert Coombes, Stephen |
| author_facet | Nicks, Rachel Allen, Robert Coombes, Stephen |
| contents | 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 utilises the method of harmonic balance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17356 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Phase and amplitude responses for delay equations using harmonic balance Nicks, Rachel Allen, Robert Coombes, Stephen Dynamical Systems 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 utilises the method of harmonic balance. |
| title | Phase and amplitude responses for delay equations using harmonic balance |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2404.17356 |