Global phase-amplitude description of oscillatory dynamics via the parameterization method

Numerical phase reduction beyond the first order approximation

(2019) Michael Rosenblum et al.   CHAOS

A Geometric Approach to Phase Response Curves and Its Numerical Computation Through the Parameterization Method

(2019) Alberto Pérez-Cervera et al.   JOURNAL OF NONLINEAR SCIENCE

Recent advances in coupled oscillator theory

(2019) Bard Ermentrout et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES

Phase-locked states in oscillating neural networks and their role in neural communication

(2019) Alberto Pérez-Cervera et al.   Communications in Nonlinear Science and Numerical Simulation

Phase-amplitude dynamics in terms of extended response functions: Invariant curves and arnold tongues

(2019) Oriol Castejón et al.   Communications in Nonlinear Science and Numerical Simulation

Optimal phase control of biological oscillators using augmented phase reduction

(2018) Bharat Monga et al.   BIOLOGICAL CYBERNETICS

Phase reduction and phase-based optimal control for biological systems: a tutorial

(2018) Bharat Monga et al.   BIOLOGICAL CYBERNETICS

Global computation of phase-amplitude reduction for limit-cycle dynamics

(2018) A. Mauroy et al.   CHAOS

Greater accuracy and broadened applicability of phase reduction using isostable coordinates

(2017) Dan Wilson et al.   JOURNAL OF MATHEMATICAL BIOLOGY

Firing rate equations require a spike synchrony mechanism to correctly describe fast oscillations in inhibitory networks

(2017) Federico Devalle et al.   PLoS Computational Biology

Global Stability Analysis Using the Eigenfunctions of the Koopman Operator

(2016) Alexandre Mauroy et al.   IEEE TRANSACTIONS ON AUTOMATIC CONTROL

Weakly coupled oscillators in a slowly varying world

(2016) Youngmin Park et al.   JOURNAL OF COMPUTATIONAL NEUROSCIENCE

Computing (Un)stable Manifolds with Validated Error Bounds: Non-resonant and Resonant Spectra

(2016) Jan Bouwe van den Berg et al.   JOURNAL OF NONLINEAR SCIENCE

A Fast Eulerian Approach for Computation of Global Isochrons in High Dimensions

(2016) Miles Detrixhe et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Phasic Burst Stimulation: A Closed-Loop Approach to Tuning Deep Brain Stimulation Parameters for Parkinson’s Disease

(2016) Abbey B. Holt et al.   PLoS Computational Biology

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

(2016) Peter Ashwin et al.   Journal of Mathematical Neuroscience

Phase-resetting as a tool of information transmission

(2015) Carmen C Canavier   CURRENT OPINION IN NEUROBIOLOGY

Phase reduction of a limit cycle oscillator perturbed by a strong amplitude-modulated high-frequency force

(2015) Kestutis Pyragas et al.   PHYSICAL REVIEW E

Parameterization of Invariant Manifolds for Periodic Orbits I: Efficient Numerics via the Floquet Normal Form

(2015) Roberto Castelli et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Phase-dependent modulation as a novel approach for therapeutic brain stimulation

(2015) Ramin Azodi-Avval et al.   Frontiers in Computational Neuroscience

Macroscopic Description for Networks of Spiking Neurons

(2015) Ernest Montbrió et al.   Physical Review X

Asymptotic Phase for Stochastic Oscillators

(2014) Peter J. Thomas et al.   PHYSICAL REVIEW LETTERS

Isostables, isochrons, and Koopman spectrum for the action–angle representation of stable fixed point dynamics

(2013) A. Mauroy et al.   PHYSICA D-NONLINEAR PHENOMENA

Phase Description of Stochastic Oscillations

(2013) Justus T. C. Schwabedal et al.   PHYSICAL REVIEW LETTERS

Computation of Limit Cycles and Their Isochrons: Fast Algorithms and Their Convergence

(2013) Gemma Huguet et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Phase-Amplitude Descriptions of Neural Oscillator Models

(2013) Kyle CA Wedgwood et al.   Journal of Mathematical Neuroscience

Phase-Amplitude Response Functions for Transient-State Stimuli

(2013) Oriol Castejón et al.   Journal of Mathematical Neuroscience

On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics

(2012) A. Mauroy et al.   CHAOS

Applied Koopmanism

(2012) Marko Budišić et al.   CHAOS

Mechanisms for Phase Shifting in Cortical Networks and their Role in Communication through Coherence

(2010) Paul H. Tiesinga et al.   Frontiers in Human Neuroscience

Quadratic Approximations for the Isochrons of Oscillators: A General Theory, Advanced Numerical Methods, and Accurate Phase Computations

(2010) Önder Suvak et al.   IEEE TRANSACTIONS ON COMPUTER-AIDED DESIGN OF INTEGRATED CIRCUITS AND SYSTEMS

Higher order approximation of isochrons

(2010) Daisuke Takeshita et al.   NONLINEARITY

Phase-response curves and synchronized neural networks

(2010) R. M. Smeal et al.   PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY B-BIOLOGICAL SCIENCES

Continuation-based Computation of Global Isochrons

(2010) Hinke M. Osinga et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Phase-Resetting Curves Determine Synchronization, Phase Locking, and Clustering in Networks of Neural Oscillators

(2009) S. Achuthan et al.   JOURNAL OF NEUROSCIENCE

A Computational and Geometric Approach to Phase Resetting Curves and Surfaces

(2009) Antoni Guillamon et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS