All Outputs (5)

Neural fields with sigmoidal firing rates: Approximate solutions (2010)
Journal Article
Coombes, S., & Schmidt, H. (2010). Neural fields with sigmoidal firing rates: Approximate solutions. Discrete and Continuous Dynamical Systems - Series A, 28(4), 1369-1379. https://doi.org/10.3934/dcds.2010.28.1369

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of... Read More about Neural fields with sigmoidal firing rates: Approximate solutions.

Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks (2010)
Journal Article
Hlinka, J., Hlinka, J., & Coombes, S. (2010). Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks. Physical Review Letters, 104(6), https://doi.org/10.1103/PhysRevLett.104.068101

Ultraslow fluctuations (0.01-0.1 Hz) are a feature of intrinsic brain activity of as yet unclear origin. We propose a candidate mechanism based on retrograde endocannabinoid signaling in a synaptically coupled network of excitatory neurons. This is k... Read More about Depolarization induced suppression of excitation and the emergence of ultraslow rhythms in neural networks.

Large-scale neural dynamics: Simple and complex (2010)
Journal Article
Coombes, S. (2010). Large-scale neural dynamics: Simple and complex. NeuroImage, 52(3), 731-739. https://doi.org/10.1016/j.neuroimage.2010.01.045

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models... Read More about Large-scale neural dynamics: Simple and complex.

Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map (2010)
Journal Article
Laudanski, J., Sumner, C., & Coombes, S. (2010). Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map. Physical Review E, 82(1), Article e011924. https://doi.org/10.1103/PhysRevE.82.011924

Thalamocortical (TC) neurones are known to express the low-voltage activated, inactivating Ca2+ current IT. The triggering of this current underlies the generation of low threshold Ca2+ potentials that may evoke single or bursts of action potentials.... Read More about Calcium window currents, periodic forcing and chaos: understanding single neuron response with a discontinuous one-dimensional map.

Understanding cardiac alternans: a piecewise linear modeling framework (2010)
Journal Article
Thul, R., & Coombes, S. (2010). Understanding cardiac alternans: a piecewise linear modeling framework. Chaos, 20, https://doi.org/10.1063/1.3518362

Cardiac alternans is a beat-to-beat alternation in action potential duration (APD) and intracellular calcium (Ca²⁺) cycling seen in cardiac myocytes under rapid pacing that is believed to be a precursor to fibrillation. The cellular mechanisms of the... Read More about Understanding cardiac alternans: a piecewise linear modeling framework.