Skip to main content

Research Repository

Advanced Search

Phase and amplitude responses for delay equations using harmonic balance

Nicks, R.; Allen, R.; Coombes, S.

Phase and amplitude responses for delay equations using harmonic balance Thumbnail


Authors

R. Allen



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.

Citation

Nicks, R., Allen, R., & Coombes, S. (2024). Phase and amplitude responses for delay equations using harmonic balance. Physical Review E, 110(1), Article L012202. https://doi.org/10.1103/PhysRevE.110.L012202

Journal Article Type Article
Acceptance Date Jun 28, 2024
Online Publication Date Jul 11, 2024
Publication Date 2024-07
Deposit Date Jul 4, 2024
Publicly Available Date Jul 11, 2024
Journal Physical Review E
Print ISSN 2470-0045
Electronic ISSN 2470-0053
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 110
Issue 1
Article Number L012202
DOI https://doi.org/10.1103/PhysRevE.110.L012202
Keywords Dynamics of networks; Coupled oscillators; Nonlinear time-delay systems; Linear response theory; Phase oscillator models
Public URL https://nottingham-repository.worktribe.com/output/36872077
Publisher URL https://journals.aps.org/pre/abstract/10.1103/PhysRevE.110.L012202

Files





You might also like



Downloadable Citations