ArticleJournal of mathematical neuroscience2016
Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience.
Article in Journal of mathematical neuroscience, 2016. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 57 papers.
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Who cites it
57 citing papers in PubMed.
- Trial
- Biophysically inspired mean-field model of neuronal populations driven by ion-exchange mechanisms.eLife · 2026Article
- Article
- A subject-specific mechanistic model of affect links electroencephalography, cardiorespiratory feedback, and monoaminergic dynamics.Frontiers in computational neuroscience · 2026Article
- Understanding the high-order network plasticity mechanisms of ultrasound neuromodulation.PLoS computational biology · 2025Article
- Multi-Shank 1024 Channels Active SiNAPS Probe for Large Multi-Regional Topographical Electrophysiological Mapping of Neural Dynamics.Advanced science (Weinheim, Baden-Wurttemberg, Germany) · 2025Article
- Direct and Retrograde Wave Propagation in Unidirectionally Coupled Wilson-Cowan Oscillators.Physical review letters · 2025Article
- The functional role of oscillatory dynamics in neocortical circuits: A computational perspective.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Digitoids: a novel computational platform for mimicking oxygen-dependent firing of neuronsFrontiers in neuroinformatics · 2025Article
- A Phase Model of the Bio-Inspired NbOx Local Active Memristor under Weak Coupling Conditions.Micromachines · 2024Article
- Coupling allows robust mammalian redox circadian rhythms despite heterogeneity and noise.Heliyon · 2024Article
- Computer-Assisted Proofs of Hopf Bubbles and Degenerate Hopf Bifurcations.Journal of dynamics and differential equations · 2024Article
- Mean-Field Approximations With Adaptive Coupling for Networks With Spike-Timing-Dependent Plasticity.Neural computation · 2023Article
- Complex spatiotemporal oscillations emerge from transverse instabilities in large-scale brain networks.PLoS computational biology · 2023Article
- Article
- An extended Hilbert transform method for reconstructing the phase from an oscillatory signal.Scientific reports · 2023Article
- Intrinsic macroscale oscillatory modes driving long range functional connectivity in female rat brains detected by ultrafast fMRI.Nature communications · 2023Article
- Dysfunctional connectivity as a neurophysiologic mechanism of disorders of consciousness: a systematic review.Frontiers in neuroscience · 2023Review
- Heteroclinic networks for brain dynamics.Frontiers in network physiology · 2023Review
- Generic generation of noise-driven chaos in stochastic time delay systems: Bridging the gap with high-end simulations.Science advances · 2022Article
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3 authors.
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Abstract
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the presence of strong coupling, or must be carefully interpreted, as in the presence of stochastic forcing. There are also surprises in the dynamical complexity of the attractors that can robustly appear-for example, heteroclinic network attractors. In this review we present a set of mathematical tools that are suitable for addressing the dynamics of oscillatory neural networks, broadening from a standard phase oscillator perspective to provide a practical framework for further successful applications of mathematics to understanding network dynamics in neuroscience.
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Registered trials
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