Phase and amplitude responses for delay equations using harmonic balance

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

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