Shape versus Timing: Linear Responses of a Limit Cycle with Hard Boundaries under Instantaneous and Static Perturbation

DOI10.1137/20M1344974zbMath1482.34047arXiv1906.04387OpenAlexW3153334302MaRDI QIDQ5004088

Hillel J. Chiel, Jeffrey P. Gill, Peter J. Thomas, Yangyang Wang

Publication date: 30 July 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.04387

zbMATH Keywords

nonsmooth systemsinfinitesimal phase response curvevariational dynamic

Mathematics Subject Classification ID

Nonsmooth analysis (49J52) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Perturbations of ordinary differential equations (34D10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Applications of variational problems to control theory (58E25)

Related Items

A direct method approach for data-driven inference of high accuracy adaptive phase-isostable reduced order models, Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems, An Adaptive Phase-Amplitude Reduction Framework without $\mathcal{O}(\epsilon)$ Constraints on Inputs, A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves

Uses Software

• AUTO
• AUTO-07P
• XPPAUT

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