All Outputs (91)

Whole brain functional connectivity: Insights from next generation neural mass modelling incorporating electrical synapses (2024)
Journal Article
Forrester, M., Petros, S., Cattell, O., Lai, Y. M., O’Dea, R. D., Sotiropoulos, S., & Coombes, S. (2024). Whole brain functional connectivity: Insights from next generation neural mass modelling incorporating electrical synapses. PLoS Computational Biology, 20(12), Article e1012647. https://doi.org/10.1371/journal.pcbi.1012647

The ready availability of brain connectome data has both inspired and facilitated the modelling of whole brain activity using networks of phenomenological neural mass models that can incorporate both interaction strength and tract length between brai... Read More about Whole brain functional connectivity: Insights from next generation neural mass modelling incorporating electrical synapses.

Oscillatory networks: insights from piecewise-linear modelling (2024)
Journal Article
Coombes, S., Şayli, M., Thul, R., Nicks, R., Porter, M. A., & Lai, Y. M. (2024). Oscillatory networks: insights from piecewise-linear modelling. SIAM Review, 66(4), 619-679. https://doi.org/10.1137/22M1534365

There is enormous interest-both mathematically and in diverse applications-in understanding the dynamics of coupled-oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology, and more. It is... Read More about Oscillatory networks: insights from piecewise-linear modelling.

Phase and amplitude responses for delay equations using harmonic balance (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Phase and amplitude responses for delay equations using harmonic balance. Physical Review E, 110(1), Article L012202. https://doi.org/10.1103/PhysRevE.110.L012202

Robust delay induced oscillations, common in nature, are often modeled by delay-differential equations (DDEs). Motivated by the success of phase-amplitude reductions for ordinary differential equations with limit cycle oscillations, there is now a gr... Read More about Phase and amplitude responses for delay equations using harmonic balance.

Stability analysis of electrical microgrids and their control systems (2024)
Journal Article
Smith, O., Coombes, S., & O'Dea, R. D. (2024). Stability analysis of electrical microgrids and their control systems. PRX Energy, 3(1), Article 013011. https://doi.org/10.1103/PRXEnergy.3.013011

The drive towards renewable energy generation is causing fundamental changes in both the structure and dynamics of power grids. Their topology is becoming increasingly decentralised due to distributed, embedded generation, and the emergence of microg... Read More about Stability analysis of electrical microgrids and their control systems.

Insights into oscillator network dynamics using a phase-isostable framework (2024)
Journal Article
Nicks, R., Allen, R., & Coombes, S. (2024). Insights into oscillator network dynamics using a phase-isostable framework. Chaos: An Interdisciplinary Journal of Nonlinear Science, 34(1), Article 013141. https://doi.org/10.1063/5.0179430

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviors under the variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by the evolu... Read More about Insights into oscillator network dynamics using a phase-isostable framework.

Understanding the effect of white matter delays on large scale brain synchrony (2024)
Journal Article
Şaylı, M., & Coombes, S. (2024). Understanding the effect of white matter delays on large scale brain synchrony. Communications in Nonlinear Science and Numerical Simulation, 131, Article 107803. https://doi.org/10.1016/j.cnsns.2023.107803

The presence of myelin is a powerful structural factor that controls the conduction speed of mammalian axons. It is the combination of local synaptic activity and non-local delayed axonal interactions within the cortex that is believed to be the majo... Read More about Understanding the effect of white matter delays on large scale brain synchrony.

Next generation neural population models (2023)
Journal Article
Coombes, S. (2023). Next generation neural population models. Frontiers in Applied Mathematics and Statistics, 9, Article 112822. https://doi.org/10.3389/fams.2023.1128224

Low-dimensional neural mass models are often invoked to model the coarse-grained activity of large populations of neurons and synapses and have been used to help understand the coordination of large scale brain rhythms. However, they are phenomenolog... Read More about Next generation neural population models.

The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective (2022)
Journal Article
Şaylı, M., Skeldon, A. C., Thul, R., Nicks, R., & Coombes, S. (2023). The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective. Physica D: Nonlinear Phenomena, 444, Article 133595. https://doi.org/10.1016/j.physd.2022.133595

Since its inception four decades ago the two-process model introduced by Borbély has provided the conceptual framework to explain sleep–wake regulation across many species, including humans. At its core, high level notions of circadian and homeostati... Read More about The two-process model for sleep–wake regulation: A nonsmooth dynamics perspective.

Structure-function clustering in weighted brain networks (2022)
Journal Article
Crofts, J. J., Forrester, M., Coombes, S., & O’Dea, R. D. (2022). Structure-function clustering in weighted brain networks. Scientific Reports, 12(1), Article 16793. https://doi.org/10.1038/s41598-022-19994-9

Functional networks, which typically describe patterns of activity taking place across the cerebral cortex, are widely studied in neuroscience. The dynamical features of these networks, and in particular their deviation from the relatively static str... Read More about Structure-function clustering in weighted brain networks.

Neural fields with rebound currents: Novel routes to patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural fields with rebound currents: Novel routes to patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. Replicating this success for subcortical tissues, such as the thalamus, r... Read More about Neural fields with rebound currents: Novel routes to patterning.

Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models (2021)
Journal Article
Tewarie, P., Prasse, B., Meier, J. M., Byrne, Á., De Domenico, M., Stam, C. J. (., Brookes, M. J., Hillebrand, A., Daffertshofer, A., Coombes, S., & Van Mieghem, P. (2021). Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models. New Journal of Physics, 23(6), Article 063065. https://doi.org/10.1088/1367-2630/ac066d

Large-scale neurophysiological networks are often reconstructed from band-pass filtered time series derived from magnetoencephalography (MEG) data. Common practice is to reconstruct these networks separately for different frequency bands and to treat... Read More about Interlayer connectivity reconstruction for multilayer brain networks using phase oscillator models.

Mean-Field Models for EEG/MEG: From Oscillations to Waves (2021)
Journal Article
Byrne, Á., Ross, J., Nicks, R., & Coombes, S. (2022). Mean-Field Models for EEG/MEG: From Oscillations to Waves. Brain Topography, 35, 36–53. https://doi.org/10.1007/s10548-021-00842-4

Neural mass models have been used since the 1970s to model the coarse-grained activity of large populations of neurons. They have proven especially fruitful for understanding brain rhythms. However, although motivated by neurobiological consideration... Read More about Mean-Field Models for EEG/MEG: From Oscillations to Waves.

Understanding sensory induced hallucinations: From neural fields to amplitude equations (2021)
Journal Article
Nicks, R., Cocks, A., Avitabile, D., Johnston, A., & Coombes, S. (2021). Understanding sensory induced hallucinations: From neural fields to amplitude equations. SIAM Journal on Applied Dynamical Systems, 20(4), 1683-1714. https://doi.org/10.1137/20M1366885

Explorations of visual hallucinations, and in particular those of Billock and Tsou [V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA, 104 (2007), pp. 8490-8495], show that annular rings with a background flicker can induce visual hallucinatio... Read More about Understanding sensory induced hallucinations: From neural fields to amplitude equations.

Neural Fields with Rebound Currents: Novel Routes to Patterning (2021)
Journal Article
Modhara, S., Lai, Y. M., Thul, R., & Coombes, S. (2021). Neural Fields with Rebound Currents: Novel Routes to Patterning. SIAM Journal on Applied Dynamical Systems, 20(3), 1596-1620. https://doi.org/10.1137/20M1364710

The understanding of how spatio-temporal patterns of neural activity may arise in the cortex of the brain has advanced with the development and analysis of neural field models. To replicate this success for sub-cortical tissues, such as the thalamus,... Read More about Neural Fields with Rebound Currents: Novel Routes to Patterning.

Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation (2021)
Journal Article
Bast, T., Coombes, S., O’Dea, R., & Tessereau, C. (2021). Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation. Brain and Neuroscience Advances, 5, https://doi.org/10.1177/2398212820975634

Humans and non-human animals show great flexibility in spatial navigation, including the ability to return to specific locations based on as few as one single experience. To study spatial navigation in the laboratory, watermaze tasks, in which rats h... Read More about Reinforcement Learning approaches to hippocampus-dependent flexible spatial navigation.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain (2020)
Journal Article
Forrester, M., Crofts, J. J., Sotiropoulos, S. N., Coombes, S., & O'Dea, R. D. (2020). The role of node dynamics in shaping emergent functional connectivity patterns in the brain. Network Neuroscience, 4(2), 467-483. https://doi.org/10.1162/netn_a_00130

© 2020 Massachusetts Institute of Technology. The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating... Read More about The role of node dynamics in shaping emergent functional connectivity patterns in the brain.

Quasicrystal patterns in a neural field model (2020)
Journal Article
Gökçe, A., Coombes, S., & Avitabile, D. (2020). Quasicrystal patterns in a neural field model. Physical Review Research, 2(1), Article 013234. https://doi.org/10.1103/PhysRevResearch.2.013234

Doubly periodic patterns in planar neural field models have been extensively studied since the 1970s for their role in explaining geometric visual hallucinations. The study of activity patterns that lack translation invariance has received little, if... Read More about Quasicrystal patterns in a neural field model.

Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans (2020)
Journal Article
Lai, Y. M., Coombes, S., & Thul, R. (2020). Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans. Communications in Nonlinear Science and Numerical Simulation, 85, Article 105181. https://doi.org/10.1016/j.cnsns.2020.105181

In cardiac myocytes, calcium cycling links the dynamics of the membrane potential to the activation of the contractile filaments. Perturbations of the calcium signalling toolkit have been demonstrated to disrupt this connection and lead to numerous p... Read More about Calcium buffers and L-type calcium channels as modulators of cardiac subcellular alternans.

Brain-wave equation incorporating axodendritic connectivity (2020)
Journal Article
Ross, J., Margetts, M., Bojak, I., Nicks, R., Avitabile, D., & Coombes, S. (2020). Brain-wave equation incorporating axodendritic connectivity. Physical Review E, 101(2), Article 022411. https://doi.org/10.1103/PhysRevE.101.022411

©2020 American Physical Society. We introduce an integral model of a two-dimensional neural field that includes a third dimension representing space along a dendritic tree that can incorporate realistic patterns of axodendritic connectivity. For natu... Read More about Brain-wave equation incorporating axodendritic connectivity.

The role of node dynamics in shaping emergent functional connectivity patterns in the brain (2020)
Journal Article
Forrester, M., Crofts, J. J., Sotiropoulos, S., Coombes, S., & O’Dea, R. (2020). The role of node dynamics in shaping emergent functional connectivity patterns in the brain. Network Neuroscience, 4(2), 467-483. https://doi.org/10.1162/netn_a_00130

The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure–function issue, treating a system of Jansen–Rit neural-mass nodes with... Read More about The role of node dynamics in shaping emergent functional connectivity patterns in the brain.