On the relation between infinitesimal shape response curves and phase-amplitude reduction for single and coupled limit-cycle oscillators

DOI10.1137/23M1575159zbMATH Open1548.34037MaRDI QIDQ6592250

Max Kreider, Peter J. Thomas

Publication date: 24 August 2024

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

zbMATH Keywords

limit cyclesynchronizationentrainmentphase-response curveisostable coordinatesshape-response curve

Mathematics Subject Classification ID

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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Nonautonomous smooth dynamical systems (37C60) Synchronization of solutions to ordinary differential equations (34D06)

Cites Work

• Title not available (Why is that?)
• Title not available (Why is that?)
• The Hopf-van der Pol system: failure of a homotopy method
• Chemical oscillations, waves, and turbulence
• Dynamics of three coupled van der Pol oscillators with application to circadian rhythms
• Uniformly valid solution of limit cycle of the Duffing-van der Pol equation
• Mathematical foundations of neuroscience
• Isochrons and phaseless sets
• Greater accuracy and broadened applicability of phase reduction using isostable coordinates
• Phase reduction and phase-based optimal control for biological systems: a tutorial
• Linearization in the large of nonlinear systems and Koopman operator spectrum
• A homeostasis criterion for limit cycle systems based on infinitesimal shape response curves
• Quantitative comparison of the mean-return-time phase and the stochastic asymptotic phase for noisy oscillators
• Phase-amplitude descriptions of neural oscillator models
• Phase-amplitude response functions for transient-state stimuli
• 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
• A fast Eulerian approach for computation of global isochrons in high dimensions
• Entrainment Control of Phase Dynamics
• Continuation-based Computation of Global Isochrons
• A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
• The Normal Modes of Nonlinear n-Degree-of-Freedom Systems
• Normal Modes for Non-Linear Vibratory Systems
• Normal Modes of Vibration for Non-Linear Continuous Systems
• A New Frame for an Old (Phase) Portrait: Finding Rivers and Other Flow Features in the Plane
• On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
• Shape versus Timing: Linear Responses of a Limit Cycle with Hard Boundaries under Instantaneous and Static Perturbation
• Global phase-amplitude description of oscillatory dynamics via the parameterization method
• High-Order Accuracy Computation of Coupling Functions for Strongly Coupled Oscillators
• A Partial Differential Equation for the Mean--Return-Time Phase of Planar Stochastic Oscillators
• Finite Dimensional Linear Systems
• Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form

This page was built for publication: On the relation between infinitesimal shape response curves and phase-amplitude reduction for single and coupled limit-cycle oscillators

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6592250)