All Outputs (87)

Waves, bumps, and patterns in neural field theories
Journal Article
Coombes, S. (2005). Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nat... Read More about Waves, bumps, and patterns in neural field theories.

Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework
Journal Article
Timofeeva, Y., Lord, G., & Coombes, S. (2005). Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework

The spike-diffuse-spike (SDS) model describes a passive dendritic tree with active dendritic spines. Spine-head dynamics is modelled with a simple integrate-and-fire process, whilst communication between spines is mediated by the cable equation. Her... Read More about Dendritic cable with active spines: a modeling study in the spike-diffuse-spike framework.

The importance of different timings of excitatory and inhibitory pathways in neural field models
Journal Article
Laing, C., & Coombes, S. (2005). The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using... Read More about The importance of different timings of excitatory and inhibitory pathways in neural field models.

Existence and wandering of bumps in a spiking neural network model
Journal Article
Chow, C., & Coombes, S. (2006). Existence and wandering of bumps in a spiking neural network model

We study spatially localized states of a spiking neuronal network populated by a pulse coupled phase oscillator known as the lighthouse model. We show that in the limit of slow synaptic interactions in the continuum limit the dynamics reduce to tho... Read More about Existence and wandering of bumps in a spiking neural network model.

Toward blueprints for network architecture, biophysical dynamics, and signal transduction
Journal Article
Coombes, S., Doiron, B., Josic, K., & Shea-Brown, E. (2006). Toward blueprints for network architecture, biophysical dynamics, and signal transduction

We review mathematical aspects of biophysical dynamics, signal transduction and network architecture that have been used to uncover functionally significant relations between the dynamics of single neurons and the networks they compose. We focus on... Read More about Toward blueprints for network architecture, biophysical dynamics, and signal transduction.

Using computational models to relate structural and functional brain connectivity
Journal Article
Hlinka, J., & Coombes, S. Using computational models to relate structural and functional brain connectivity. European Journal of Neuroscience, 36(2), https://doi.org/10.1111/j.1460-9568.2012.08081.x

Modern imaging methods allow a non-invasive assessment of both structural and functional brain connectivity. This has lead to the identification of disease-related alterations affecting functional connectivity. The mechanism of how such alterations... Read More about Using computational models to relate structural and functional brain connectivity.

Phase-amplitude descriptions of neural oscillator models
Journal Article
Wedgwood, K. C., Lin, K. K., Thul, R., & Coombes, S. Phase-amplitude descriptions of neural oscillator models. Journal of Mathematical Neuroscience, 3(2), https://doi.org/10.1186/2190-8567-3-2

Phase oscillators are a common starting point for the reduced description of many single neuron models that exhibit a strongly attracting limit cycle. The framework for analysing such models in response to weak perturbations is now particularly well... Read More about Phase-amplitude descriptions of neural oscillator models.