A Continuation Approach to Computing Phase Resetting Curves

DOI10.1007/978-3-030-51264-4_1zbMath1454.37082arXiv2003.06937OpenAlexW3043948612MaRDI QIDQ5131670

Bernd Krauskopf, Peter Langfield, Hinke M. Osinga

Publication date: 9 November 2020

Published in: Advances in Dynamics, Optimization and Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2003.06937

zbMATH Keywords

phase resettingphase resetting curvesmulti-segment boundary value problemoscillating neurons

Mathematics Subject Classification ID

Simulation of dynamical systems (37M05) Computational methods for invariant manifolds of dynamical systems (37M21)

Related Items (1)

Methods of continuation and their implementation in the COCO software platform with application to delay differential equations

Uses Software

• AUTO
• AUTO-07P

Cites Work

• Unnamed Item
• Mathematical foundations of neuroscience
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Isochrons and phaseless sets
• Patterns of phase compromise in biological cycles
• Phase reduction and phase-based optimal control for biological systems: a tutorial
• Phase-dependence of response curves to deep brain stimulation and their relationship: from essential tremor patient data to a Wilson-Cowan model
• Apparent discontinuities in the phase-resetting response of cardiac pacemakers
• Phase-amplitude dynamics in terms of extended response functions: invariant curves and Arnold tongues
• Phase-amplitude descriptions of neural oscillator models
• Phase-amplitude response functions for transient-state stimuli
• A geometric approach to phase response curves and its numerical computation through the parameterization method
• Extreme phase sensitivity in systems with fractal isochrons
• The Shape of Phase-Resetting Curves in Oscillators with a Saddle Node on an Invariant Circle Bifurcation
• Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence
• Global Isochrons and Phase Sensitivity of Bursting Neurons
• On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
• Continuation-based Computation of Global Isochrons
• Forward-Time and Backward-Time Isochrons and Their Interactions
• A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
• A Lin's method approach to finding and continuing heteroclinic connections involving periodic orbits
• Solving Winfree's puzzle: The isochrons in the FitzHugh-Nagumo model
• On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
• Augmented Phase Reduction of (Not So) Weakly Perturbed Coupled Oscillators
• Continuation-Based Numerical Detection of After-Depolarization and Spike-Adding Thresholds

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