Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
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Title
Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review
Authors
Keywords
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Journal
Journal of Mathematical Neuroscience
Volume 10, Issue 1, Pages -
Publisher
Springer Science and Business Media LLC
Online
2020-05-27
DOI
10.1186/s13408-020-00086-9
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Note: Only part of the references are listed.- The effects of within-neuron degree correlations in networks of spiking neurons
- (2020) Carlo R. Laing et al. BIOLOGICAL CYBERNETICS
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- (2019) Áine Byrne et al. JOURNAL OF NEUROPHYSIOLOGY
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- (2018) Christian Bick et al. CHAOS
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- (2018) Helge Dietert et al. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
- On the nature and use of models in network neuroscience
- (2018) Danielle S. Bassett et al. NATURE REVIEWS NEUROSCIENCE
- MULAN: Evaluation and ensemble statistical inference for functional connectivity
- (2018) Huifang E. Wang et al. NEUROIMAGE
- The mathematics behind chimera states
- (2018) O E Omel’chenko NONLINEARITY
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- (2018) Felix P. Kemeth et al. PHYSICAL REVIEW LETTERS
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- (2018) Irina V. Tyulkina et al. PHYSICAL REVIEW LETTERS
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- (2018) Carlo R. Laing Journal of Mathematical Neuroscience
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- Synchronization and equitable partitions in weighted networks
- (2018) Manuela A. D. Aguiar et al. CHAOS
- Seizure prediction — ready for a new era
- (2018) Levin Kuhlmann et al. Nature Reviews Neurology
- Transition from Asynchronous to Oscillatory Dynamics in Balanced Spiking Networks with Instantaneous Synapses
- (2018) Matteo di Volo et al. PHYSICAL REVIEW LETTERS
- Network mechanisms underlying the role of oscillations in cognitive tasks
- (2018) Helmut Schmidt et al. PLoS Computational Biology
- Macroscopic models for networks of coupled biological oscillators
- (2018) Kevin M. Hannay et al. Science Advances
- Collective mode reductions for populations of coupled noisy oscillators
- (2018) Denis S. Goldobin et al. CHAOS
- Structure preserving schemes for the continuum Kuramoto model: Phase transitions
- (2018) José A. Carrillo et al. JOURNAL OF COMPUTATIONAL PHYSICS
- The WS transform for the Kuramoto model with distributed amplitudes, phase lag and time delay
- (2017) M A Lohe Journal of Physics A-Mathematical and Theoretical
- Hyperbolic geometry of Kuramoto oscillator networks
- (2017) Bolun Chen et al. Journal of Physics A-Mathematical and Theoretical
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- (2017) Jonathan M. Levine et al. NATURE
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- (2017) Agostina Palmigiano et al. NATURE NEUROSCIENCE
- Dynamic models of large-scale brain activity
- (2017) Michael Breakspear NATURE NEUROSCIENCE
- Network neuroscience
- (2017) Danielle S Bassett et al. NATURE NEUROSCIENCE
- Single or multiple frequency generators in on-going brain activity: A mechanistic whole-brain model of empirical MEG data
- (2017) Gustavo Deco et al. NEUROIMAGE
- Asynchronous networks and event driven dynamics
- (2017) Christian Bick et al. NONLINEARITY
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- (2017) Christian Bick et al. PHYSICAL REVIEW LETTERS
- Coupling functions: Universal insights into dynamical interaction mechanisms
- (2017) Tomislav Stankovski et al. REVIEWS OF MODERN PHYSICS
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- (2017) Federico Devalle et al. PLoS Computational Biology
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- (2017) Murat Demirtaş et al. NeuroImage-Clinical
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- (2016) Carlo R. Laing CHAOS
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- (2016) Helmut Schmidt et al. EPILEPSIA
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- (2014) Cornelis J. Stam NATURE REVIEWS NEUROSCIENCE
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- (2014) Björn Kralemann et al. NEW JOURNAL OF PHYSICS
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- (2014) Tiago Pereira et al. NONLINEARITY
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- (2012) Mark Wildie et al. CHAOS
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- (2012) Christian Rummel et al. NEUROINFORMATICS
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- (2012) Hyunsuk Hong et al. PHYSICAL REVIEW E
- Temporal networks
- (2012) Petter Holme et al. PHYSICS REPORTS-REVIEW SECTION OF PHYSICS LETTERS
- Comment on “Long time evolution of phase oscillator systems” [Chaos 19, 023117 (2009)]
- (2011) Edward Ott et al. CHAOS
- PHASE OSCILLATORS WITH SINUSOIDAL COUPLING INTERPRETED IN TERMS OF PROJECTIVE GEOMETRY
- (2011) IAN STEWART INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
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- (2011) Pedro A. Valdes-Sosa et al. NEUROIMAGE
- Role of local network oscillations in resting-state functional connectivity
- (2011) Joana Cabral et al. NEUROIMAGE
- Dynamics of heterogeneous oscillator ensembles in terms of collective variables
- (2011) Arkady Pikovsky et al. PHYSICA D-NONLINEAR PHENOMENA
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- (2011) Maxim Komarov et al. PHYSICAL REVIEW E
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- (2011) Hyunsuk Hong et al. PHYSICAL REVIEW E
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- (2011) Takuma Tanaka et al. PHYSICAL REVIEW LETTERS
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- (2011) Hyunsuk Hong et al. PHYSICAL REVIEW LETTERS
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- (2010) Christopher J. Honey et al. NEUROIMAGE
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- (2010) Erik A. Martens PHYSICAL REVIEW E
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- (2010) Michael Monteforte et al. PHYSICAL REVIEW LETTERS
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- (2010) Xiao-Jing Wang PHYSIOLOGICAL REVIEWS
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- Quantitative prediction of intermittent high-frequency oscillations in neural networks with supralinear dendritic interactions
- (2010) R.-M. Memmesheimer PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
- Neuronal Gamma-Band Synchronization as a Fundamental Process in Cortical Computation
- (2009) Pascal Fries Annual Review of Neuroscience
- The Wilson–Cowan model, 36 years later
- (2009) Alain Destexhe et al. BIOLOGICAL CYBERNETICS
- Long time evolution of phase oscillator systems
- (2009) Edward Ott et al. CHAOS
- Chimera states in heterogeneous networks
- (2009) Carlo R. Laing CHAOS
- Identical phase oscillators with global sinusoidal coupling evolve by Möbius group action
- (2009) Seth A. Marvel et al. CHAOS
- Synchronization phenomena in human epileptic brain networks
- (2009) Klaus Lehnertz et al. JOURNAL OF NEUROSCIENCE METHODS
- A comparative study of synchrony measures for the early diagnosis of Alzheimer's disease based on EEG
- (2009) J. Dauwels et al. NEUROIMAGE
- Existence of hysteresis in the Kuramoto model with bimodal frequency distributions
- (2009) Diego Pazó et al. PHYSICAL REVIEW E
- Exact results for the Kuramoto model with a bimodal frequency distribution
- (2009) E. A. Martens et al. PHYSICAL REVIEW E
- Large Coupled Oscillator Systems with Heterogeneous Interaction Delays
- (2009) Wai Shing Lee et al. PHYSICAL REVIEW LETTERS
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- (2008) Jean-Christophe Leloup et al. BIOESSAYS
- Low dimensional behavior of large systems of globally coupled oscillators
- (2008) Edward Ott et al. CHAOS
- Synchronization in networks of networks: The onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators
- (2008) Ernest Barreto et al. PHYSICAL REVIEW E
- Partially Integrable Dynamics of Hierarchical Populations of Coupled Oscillators
- (2008) Arkady Pikovsky et al. PHYSICAL REVIEW LETTERS
- Solvable Model for Chimera States of Coupled Oscillators
- (2008) Daniel M. Abrams et al. PHYSICAL REVIEW LETTERS
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- (2008) S. Coombes SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS
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