Phase reduction and phase-based optimal control for biological systems: a tutorial
type: Item
instance of: scholarly article
title: Phase reduction and phase-based optimal control for biological systems: a tutorial
zbMATH Open document ID: 1411.92122
author: Bharat Monga
author: Dan Wilson
author: Tim Matchen
author: Jeff Moehlis
published in: Biological Cybernetics
publication date: 2019-03-27T00:00:00Z
Mathematics Subject Classification ID: 92C42
Mathematics Subject Classification ID: 49N90
Mathematics Subject Classification ID: 35Q92
zbMATH DE Number: 7043353
zbMATH Keywords: phase reduction
zbMATH Keywords: optimal control
zbMATH Keywords: nonlinear oscillators
zbMATH Keywords: control of biological systems
Wikidata QID: Q91375719
describes a project that uses: XPPAUT
MaRDI profile type: Publication
full work available at URL: s00422-018-0780-z
OpenAlex ID: W2889667300
cites work: On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
cites work: The parameterization method for invariant manifolds. III: Overview and applications
cites work: Phase-amplitude response functions for transient-state stimuli
cites work: Q5848416
cites work: Partial phase synchronization of neural populations due to random Poisson inputs
cites work: Event-based minimum-time control of oscillatory neuron models
cites work: Charge-balanced spike timing control for phase models of spiking neurons
cites work: Constrained charge-balanced minimum-power controls for spiking neuron oscillators
cites work: A fast Eulerian approach for computation of global isochrons in high dimensions
cites work: Simulating, Analyzing, and Animating Dynamical Systems
cites work: The shape of phase-resetting curves in oscillators with a saddle node on an invariant circle bifurcation
cites work: Frequency Plateaus in a Chain of Weakly Coupled Oscillators, I.
cites work: Multiple pulse interactions and averaging in systems of coupled neural oscillators
cites work: Mathematical foundations of neuroscience
cites work: Starting, stopping, and resetting biological oscillators: in search of optimum perturbations
cites work: Continuous-time control of alternans in long Purkinje fibers
cites work: Q3993559
cites work: Stability, Instability and Chaos
cites work: Q3953228
cites work: Q4001253
cites work: Isochrons and phaseless sets
cites work: Phase Portraits of Planar Vector Fields: Computer Proofs
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
cites work: Weakly connected neural networks
cites work: Phase locking of biological clocks
cites work: Computation of limit cycles and their isochrons: fast algorithms and their convergence
cites work: Phase Equations for Relaxation Oscillators
cites work: Engineering Complex Dynamical Structures: Sequential Patterns and Desynchronization
cites work: Plane Wave Solutions to Reaction-Diffusion Equations
cites work: Chemical oscillations, waves, and turbulence
cites work: Elements of applied bifurcation theory.
cites work: Solving Winfree's puzzle: The isochrons in the FitzHugh-Nagumo model
cites work: Forward-Time and Backward-Time Isochrons and Their Interactions
cites work: Q3446096
cites work: Q5802833
cites work: Phase model-based neuron stabilization into arbitrary clusters
cites work: Global computation of phase-amplitude reduction for limit-cycle dynamics
cites work: On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
cites work: Isostables, isochrons, and Koopman spectrum for the action-angle representation of stable fixed point dynamics
cites work: Global isochrons and phase sensitivity of bursting neurons
cites work: Improving the precision of noisy oscillators
cites work: Optimal phase control of biological oscillators using augmented phase reduction
cites work: Minimum energy desynchronizing control for coupled neurons
cites work: Time optimal control of spiking neurons
cites work: Continuation-based Computation of Global Isochrons
cites work: Appropriate initial conditions for asymptotic descriptions of the long term evolution of dynamical systems
cites work: Phase Resetting in an Asymptotically Phaseless System: On the Phase Response of Limit Cycles Verging on a Heteroclinic Orbit
cites work: Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems
cites work: Optimal control formulation of pulse-based control using Koopman operator
cites work: Higher order approximation of isochrons
cites work: Phase resetting in medicine and biology. Stochastic modelling and data analysis
cites work: A model of desynchronizing deep brain stimulation with a demand-controlled coordinated reset of neural subpopulations
cites work: Phase-amplitude descriptions of neural oscillator models
cites work: Normally hyperbolic invariant manifolds in dynamical systems
cites work: An Operational Definition of Phase Characterizes the Transient Response of Perturbed Limit Cycle Oscillators
cites work: Greater accuracy and broadened applicability of phase reduction using isostable coordinates

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: An energy-optimal methodology for synchronization of excitable media

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: Locally optimal extracellular stimulation for chaotic desynchronization of neural populations

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: Optimal chaotic desynchronization for neural populations

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: Extending phase reduction to excitable media: theory and applications

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: Spatiotemporal control to eliminate cardiac alternans using isostable reduction

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: Patterns of phase compromise in biological cycles

Phase reduction and phase-based optimal control for biological systems: a tutorial (cites work)
cites work: The geometry of biological time.

Phase reduction and phase-based optimal control for biological systems: a tutorial (DOI)
DOI: 10.1007/S00422-018-0780-Z