Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
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Title
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience
Authors
Keywords
Central pattern generator, Chimera state, Coupled oscillator network, Groupoid formalism, Heteroclinic cycle, Isochrons, Master stability function, Network motif, Perceptual rivalry, Phase oscillator, Phase–amplitude coordinates, Stochastic oscillator, Strongly coupled integrate-and-fire network, Symmetric dynamics, Weakly coupled phase oscillator network, Winfree model
Journal
Journal of Mathematical Neuroscience
Volume 6, Issue 1, Pages -
Publisher
Springer Nature
Online
2016-01-06
DOI
10.1186/s13408-015-0033-6
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Note: Only part of the references are listed.- Weak chimeras in minimal networks of coupled phase oscillators
- (2015) Peter Ashwin et al. CHAOS
- Chimera states: coexistence of coherence and incoherence in networks of coupled oscillators
- (2015) Mark J Panaggio et al. NONLINEARITY
- Exact Neural Fields Incorporating Gap Junctions
- (2015) Carlo R. Laing SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Extending Phase Reduction to Excitable Media: Theory and Applications
- (2015) Dan Wilson et al. SIAM REVIEW
- The ‘laws’ of binocular rivalry: 50 years of Levelt’s propositions
- (2015) J.W. Brascamp et al. VISION RESEARCH
- Cross-frequency transfer in a stochastically driven mesoscopic neuronal model
- (2015) Maciej Jedynak et al. Frontiers in Computational Neuroscience
- Network dynamics with BrainX3: a large-scale simulation of the human brain network with real-time interaction
- (2015) Xerxes D. Arsiwalla et al. Frontiers in Neuroinformatics
- Stability of a family of travelling wave solutions in a feedforward chain of phase oscillators
- (2015) O E Lanford et al. NONLINEARITY
- Synchronization in complex networks of phase oscillators: A survey
- (2014) Florian Dörfler et al. AUTOMATICA
- Cascades of Multiheaded Chimera States for Coupled Phase Oscillators
- (2014) Yuri L. Maistrenko et al. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
- Modern network science of neurological disorders
- (2014) Cornelis J. Stam NATURE REVIEWS NEUROSCIENCE
- A Transition to Sharp Timing in Stochastic Leaky Integrate-and-Fire Neurons Driven by Frozen Noisy Input
- (2014) Thibaud Taillefumier et al. NEURAL COMPUTATION
- Improving the precision of noisy oscillators
- (2014) Jeff Moehlis PHYSICA D-NONLINEAR PHENOMENA
- Clustering in globally coupled oscillators near a Hopf bifurcation: Theory and experiments
- (2014) Hiroshi Kori et al. PHYSICAL REVIEW E
- Hysteretic transitions in the Kuramoto model with inertia
- (2014) Simona Olmi et al. PHYSICAL REVIEW E
- Chimera States: The Existence Criteria Revisited
- (2014) Gautam C. Sethia et al. PHYSICAL REVIEW LETTERS
- Controlling Unstable Chaos: Stabilizing Chimera States by Feedback
- (2014) Jan Sieber et al. PHYSICAL REVIEW LETTERS
- Key Bifurcations of Bursting Polyrhythms in 3-Cell Central Pattern Generators
- (2014) Jeremy Wojcik et al. PLoS One
- Dynamics of Coupled Noisy Neural Oscillators with Heterogeneous Phase Resetting Curves
- (2014) Cheng Ly SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Chunking dynamics: heteroclinics in mind
- (2014) Mikhail I. Rabinovich et al. Frontiers in Computational Neuroscience
- Cluster synchronization and isolated desynchronization in complex networks with symmetries
- (2014) Louis M. Pecora et al. Nature Communications
- Network Symmetry and Binocular Rivalry Experiments
- (2014) Casey O Diekman et al. Journal of Mathematical Neuroscience
- Nonlinear Dynamics of Neuronal Excitability, Oscillations, and Coincidence Detection
- (2013) John Rinzel et al. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
- Mode-locking neurodynamics predict human auditory brainstem responses to musical intervals
- (2013) Karl D. Lerud et al. HEARING RESEARCH
- Salamandra Robotica II: An Amphibious Robot to Study Salamander-Like Swimming and Walking Gaits
- (2013) Alessandro Crespi et al. IEEE Transactions on Robotics
- Complete Classification of the Macroscopic Behavior of a Heterogeneous Network of Theta Neurons
- (2013) Tanushree B. Luke et al. NEURAL COMPUTATION
- On designing heteroclinic networks from graphs
- (2013) Peter Ashwin et al. PHYSICA D-NONLINEAR PHENOMENA
- Collective phase dynamics of globally coupled oscillators: Noise-induced anti-phase synchronization
- (2013) Yoji Kawamura PHYSICA D-NONLINEAR PHENOMENA
- Networks of theta neurons with time-varying excitability: Macroscopic chaos, multistability, and final-state uncertainty
- (2013) Paul So et al. PHYSICA D-NONLINEAR PHENOMENA
- Remote Synchronization Reveals Network Symmetries and Functional Modules
- (2013) Vincenzo Nicosia et al. PHYSICAL REVIEW LETTERS
- Chimera states in mechanical oscillator networks
- (2013) E. A. Martens et al. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
- On the use of Fourier averages to compute the global isochrons of (quasi)periodic dynamics
- (2012) A. Mauroy et al. CHAOS
- Feed-forward networks, center manifolds, and forcing
- (2012) Martin Golubitsky et al. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
- Seizure generation: The role of nodes and networks
- (2012) John R. Terry et al. EPILEPSIA
- Using computational models to relate structural and functional brain connectivity
- (2012) Jaroslav Hlinka et al. EUROPEAN JOURNAL OF NEUROSCIENCE
- The dynamics of neurological disease: integrating computational, experimental and clinical neuroscience
- (2012) Stephen Coombes et al. EUROPEAN JOURNAL OF NEUROSCIENCE
- The robustness of phase-locking in neurons with dendro-dendritic electrical coupling
- (2012) Michael A. Schwemmer et al. JOURNAL OF MATHEMATICAL BIOLOGY
- Limitations of perturbative techniques in the analysis of rhythms and oscillations
- (2012) Kevin K. Lin et al. JOURNAL OF MATHEMATICAL BIOLOGY
- Intrinsic heterogeneity in oscillatory dynamics limits correlation-induced neural synchronization
- (2012) Shawn D. Burton et al. JOURNAL OF NEUROPHYSIOLOGY
- The Geometry of Spontaneous Spiking in Neuronal Networks
- (2012) Georgi S. Medvedev et al. JOURNAL OF NONLINEAR SCIENCE
- Chimera and phase-cluster states in populations of coupled chemical oscillators
- (2012) Mark R. Tinsley et al. Nature Physics
- The Shape of Phase-Resetting Curves in Oscillators with a Saddle Node on an Invariant Circle Bifurcation
- (2012) G. Bard Ermentrout et al. NEURAL COMPUTATION
- Neuromodulation of Brain States
- (2012) Seung-Hee Lee et al. NEURON
- Network periodic solutions: patterns of phase-shift synchrony
- (2012) Martin Golubitsky et al. NONLINEARITY
- Phase reduction of weakly perturbed limit cycle oscillations in time-delay systems
- (2012) V. Novičenko et al. PHYSICA D-NONLINEAR PHENOMENA
- Hierarchical synchrony of phase oscillators in modular networks
- (2012) Per Sebastian Skardal et al. PHYSICAL REVIEW E
- Adjoint Method Provides Phase Response Functions for Delay-Induced Oscillations
- (2012) Kiyoshi Kotani et al. PHYSICAL REVIEW LETTERS
- Nonuniversal Transitions to Synchrony in the Sakaguchi-Kuramoto Model
- (2012) Oleh E. Omel’chenko et al. PHYSICAL REVIEW LETTERS
- Computing with Neural Synchrony
- (2012) Romain Brette PLoS Computational Biology
- The Generation of Phase Differences and Frequency Changes in a Network Model of Inferior Olive Subthreshold Oscillations
- (2012) Benjamin Torben-Nielsen et al. PLoS Computational Biology
- A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy
- (2012) Oscar Benjamin et al. Journal of Mathematical Neuroscience
- Synchrony and Asynchrony for Neuronal Dynamics Defined on Complex Networks
- (2011) R. E. Lee DeVille et al. BULLETIN OF MATHEMATICAL BIOLOGY
- Understanding cardiac alternans: A piecewise linear modeling framework
- (2011) R. Thul et al. CHAOS
- Breakdown of order preservation in symmetric oscillator networks with pulse-coupling
- (2011) Hinrich Kielblock et al. CHAOS
- Different Roles for Homologous Interneurons in Species Exhibiting Similar Rhythmic Behaviors
- (2011) Akira Sakurai et al. CURRENT BIOLOGY
- Collective chaos in pulse-coupled neural networks
- (2011) S. Olmi et al. EPL
- Recurrent events of synchrony in complex networks of pulse-coupled oscillators
- (2011) A. Rothkegel et al. EPL
- Synchronization of Coupled Limit Cycles
- (2011) Georgi S. Medvedev JOURNAL OF NONLINEAR SCIENCE
- The role of phase synchronization in memory processes
- (2011) Juergen Fell et al. NATURE REVIEWS NEUROSCIENCE
- Neural Mass Activity, Bifurcations, and Epilepsy
- (2011) Jonathan Touboul et al. NEURAL COMPUTATION
- Role of local network oscillations in resting-state functional connectivity
- (2011) Joana Cabral et al. NEUROIMAGE
- Nonsmooth dynamics in spiking neuron models
- (2011) S. Coombes et al. PHYSICA D-NONLINEAR PHENOMENA
- Cluster synchrony in systems of coupled phase oscillators with higher-order coupling
- (2011) Per Sebastian Skardal et al. PHYSICAL REVIEW E
- Correlation transfer in stochastically driven neural oscillators over long and short time scales
- (2011) Aushra Abouzeid et al. PHYSICAL REVIEW E
- Chimera states are chaotic transients
- (2011) Matthias Wolfrum et al. PHYSICAL REVIEW E
- Chaos in Symmetric Phase Oscillator Networks
- (2011) Christian Bick et al. PHYSICAL REVIEW LETTERS
- Information flow dynamics in the brain
- (2011) Mikhail I. Rabinovich et al. Physics of Life Reviews
- Multi-frequency activation of neuronal networks by coordinated reset stimulation
- (2011) B. Lysyansky et al. Interface Focus
- Emergence of structural patterns out of synchronization in networks with competitive interactions
- (2011) Salvatore Assenza et al. Scientific Reports
- Modeling Brain Resonance Phenomena Using a Neural Mass Model
- (2011) Andreas Spiegler et al. PLoS Computational Biology
- On the Influence of Amplitude on the Connectivity between Phases
- (2011) Andreas Daffertshofer et al. Frontiers in Neuroinformatics
- Criteria for robustness of heteroclinic cycles in neural microcircuits
- (2011) Peter Ashwin et al. Journal of Mathematical Neuroscience
- Stochastic synchronization of neuronal populations with intrinsic and extrinsic noise
- (2011) Paul C Bressloff et al. Journal of Mathematical Neuroscience
- Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise
- (2010) Hiroya Nakao et al. CHAOS
- From Limit Cycles to Strange Attractors
- (2010) William Ott et al. COMMUNICATIONS IN MATHEMATICAL PHYSICS
- THE EXISTENCE AND CLASSIFICATION OF SYNCHRONY-BREAKING BIFURCATIONS IN REGULAR HOMOGENEOUS NETWORKS USING LATTICE STRUCTURES
- (2010) HIROKO KAMEI INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
- CONTROL OF SYNCHRONIZATION IN COUPLED NEURAL SYSTEMS BY TIME-DELAYED FEEDBACK
- (2010) PHILIPP HÖVEL et al. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
- Synaptic patterning of left-right alternation in a computational model of the rodent hindlimb central pattern generator
- (2010) William Erik Sherwood et al. JOURNAL OF COMPUTATIONAL NEUROSCIENCE
- Dynamics of periodically kicked oscillators
- (2010) Kevin K. Lin et al. Journal of Fixed Point Theory and Applications
- Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation
- (2010) M. Aguiar et al. JOURNAL OF NONLINEAR SCIENCE
- Emerging concepts for the dynamical organization of resting-state activity in the brain
- (2010) Gustavo Deco et al. NATURE REVIEWS NEUROSCIENCE
- Dynamical equivalence of networks of coupled dynamical systems: II. General case
- (2010) N Agarwal et al. NONLINEARITY
- Dynamical equivalence of networks of coupled dynamical systems: I. Asymmetric inputs
- (2010) N Agarwal et al. NONLINEARITY
- Emergent behaviour of a generalized Viscek-type flocking model
- (2010) Seung-Yeal Ha et al. NONLINEARITY
- Higher order approximation of isochrons
- (2010) Daisuke Takeshita et al. NONLINEARITY
- Analytic approximations of statistical quantities and response of noisy oscillators
- (2010) Cheng Ly et al. PHYSICA D-NONLINEAR PHENOMENA
- Cascade-induced synchrony in stochastically driven neuronal networks
- (2010) Katherine A. Newhall et al. PHYSICAL REVIEW E
- Dynamics of Limit-Cycle Oscillators Subject to General Noise
- (2010) Denis S. Goldobin et al. PHYSICAL REVIEW LETTERS
- Synchronization of coupled stochastic limit cycle oscillators
- (2010) Georgi S. Medvedev PHYSICS LETTERS A
- Nonlinear dynamics of the brain: emotion and cognition
- (2010) Mikhail I Rabinovich et al. PHYSICS-USPEKHI
- Neurophysiological and Computational Principles of Cortical Rhythms in Cognition
- (2010) Xiao-Jing Wang PHYSIOLOGICAL REVIEWS
- Within-Burst Synchrony Changes for Coupled Elliptic Bursters
- (2010) Abul Kalam al Azad et al. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Continuation-based Computation of Global Isochrons
- (2010) Hinke M. Osinga et al. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Hypotheses on the functional roles of chaotic transitory dynamics
- (2009) Ichiro Tsuda CHAOS
- Self-organization in predominantly feedforward oscillator chains
- (2009) Stanislav M. Mintchev et al. CHAOS
- Mode-Locked Spike Trains in Responses of Ventral Cochlear Nucleus Chopper and Onset Neurons to Periodic Stimuli
- (2009) Jonathan Laudanski et al. JOURNAL OF NEUROPHYSIOLOGY
- Reliability of Coupled Oscillators
- (2009) Kevin K. Lin et al. JOURNAL OF NONLINEAR SCIENCE
- Heteroclinic Ratchets in Networks of Coupled Oscillators
- (2009) Özkan Karabacak et al. JOURNAL OF NONLINEAR SCIENCE
- Delays in activity-based neural networks
- (2009) S. Coombes et al. PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
- Semi-passivity and synchronization of diffusively coupled neuronal oscillators
- (2009) Erik Steur et al. PHYSICA D-NONLINEAR PHENOMENA
- The dynamics of chimera states in heterogeneous Kuramoto networks
- (2009) Carlo R. Laing PHYSICA D-NONLINEAR PHENOMENA
- A low-dimensional model of binocular rivalry using winnerless competition
- (2009) Peter Ashwin et al. PHYSICA D-NONLINEAR PHENOMENA
- Stochastic Phase Reduction for a General Class of Noisy Limit Cycle Oscillators
- (2009) Jun-nosuke Teramae et al. PHYSICAL REVIEW LETTERS
- Coupling of mesoscopic brain oscillations: Recent advances in analytical and theoretical perspectives
- (2009) Calvin K. Young et al. PROGRESS IN NEUROBIOLOGY
- Designing the Dynamics of Globally Coupled Oscillators
- (2009) G. Orosz et al. PROGRESS OF THEORETICAL PHYSICS
- Spatially Periodic Patterns of Synchrony in Lattice Networks
- (2009) Ana Paula S. Dias et al. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- A Computational and Geometric Approach to Phase Resetting Curves and Surfaces
- (2009) Antoni Guillamon et al. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Extracting non-linear integrate-and-fire models from experimental data using dynamic I–V curves
- (2008) Laurent Badel et al. BIOLOGICAL CYBERNETICS
- Sparsely synchronized neuronal oscillations
- (2008) Nicolas Brunel et al. CHAOS
- Neuronal synchrony: Peculiarity and generality
- (2008) Thomas Nowotny et al. CHAOS
- Polyrhythmic synchronization in bursting networking motifs
- (2008) Andrey Shilnikov et al. CHAOS
- Symmetry in complex networks
- (2008) Ben D. MacArthur et al. DISCRETE APPLIED MATHEMATICS
- Model driven EEG/fMRI fusion of brain oscillations
- (2008) Pedro A. Valdes-Sosa et al. HUMAN BRAIN MAPPING
- BURST SYNCHRONIZATION AND CHAOTIC PHENOMENA IN TWO STRONGLY COUPLED RESONATE-AND-FIRE NEURONS
- (2008) KAZUKI NAKADA et al. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
- Episodic activity in a heterogeneous excitatory network, from spiking neurons to mean field
- (2008) Boris B. Vladimirski et al. JOURNAL OF COMPUTATIONAL NEUROSCIENCE
- The effects of cholinergic neuromodulation on neuronal phase-response curves of modeled cortical neurons
- (2008) Klaus M. Stiefel et al. JOURNAL OF COMPUTATIONAL NEUROSCIENCE
- Central pattern generators for locomotion control in animals and robots: A review
- (2008) Auke Jan Ijspeert NEURAL NETWORKS
- Heteroclinic cycles between unstable attractors
- (2008) Henk Broer et al. NONLINEARITY
- Shear-induced chaos
- (2008) Kevin K Lin et al. NONLINEARITY
- Bifurcations from regular quotient networks: A first insight
- (2008) Manuela A.D. Aguiar et al. PHYSICA D-NONLINEAR PHENOMENA
- From networks of unstable attractors to heteroclinic switching
- (2008) Christoph Kirst et al. PHYSICAL REVIEW E
- Spatiotemporal coding of inputs for a system of globally coupled phase oscillators
- (2008) John Wordsworth et al. PHYSICAL REVIEW E
- Phase Reduction of Stochastic Limit Cycle Oscillators
- (2008) Kazuyuki Yoshimura et al. PHYSICAL REVIEW LETTERS
- Synchronization in complex networks
- (2008) Alex Arenas et al. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
- Neuronal Networks with Gap Junctions: A Study of Piecewise Linear Planar Neuron Models
- (2008) S. Coombes SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
- Reliability, synchrony and noise
- (2008) G. Bard Ermentrout et al. TRENDS IN NEUROSCIENCES
- Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
- (2007) Peter Ashwin et al. PHYSICA D-NONLINEAR PHENOMENA
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