Outputs (86)

Instabilities in threshold-diffusion equations with delay (2008)
Journal Article
Laing, C. R., & Coombes, S. (2009). Instabilities in threshold-diffusion equations with delay. Physica D: Nonlinear Phenomena, 238(3), 264-272. https://doi.org/10.1016/j.physd.2008.10.014

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics, ranging from periodic solutions through to spatio-temporal chaos. In this paper, we consider a class of scal... Read More about Instabilities in threshold-diffusion equations with delay.

Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models (2008)
Journal Article
Coombes, S. (2008). Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models. SIAM Journal on Applied Dynamical Systems, 7(3), 1101–1129. https://doi.org/10.1137/070707579

The presence of gap junction coupling among neurons of the central nervous systems has been appreciated for some time now. In recent years there has been an upsurge of interest from the mathematical community in understanding the contribution of the... Read More about Neuronal networks with gap junctions: A study of piece-wise linear planar neuron models.

Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis (2008)
Journal Article
Zachariou, M., Dissanayake, D. W. N., Coombes, S., Owen, M. R., & Mason, R. (in press). Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis. Cognitive Neurodynamics, 2, https://doi.org/10.1007/s11571-008-9050-4

Gating of sensory information can be assessed using an auditory conditioning-test paradigm which measures the reduction in the auditory evoked response to a test stimulus following an initial conditioning stimulus. Recording brainwaves from specific... Read More about Sensory gating and its modulation by cannabinoids: electrophysiological, computational and mathematical analysis.

Democratization in a passive dendritic tree: An analytical investigation (2008)
Journal Article
Timofeeva, Y., Cox, S. J., Coombes, S., & Josic, K. (2008). Democratization in a passive dendritic tree: An analytical investigation. Journal of Computational Neuroscience, 25(2), 228-244. https://doi.org/10.1007/s10827-008-0075-9

One way to achieve amplification of distal synaptic inputs on a dendritic tree is to scale the amplitude and/or duration of the synaptic conductance with its distance from the soma. This is an example of what is often referred to as "dendritic democr... Read More about Democratization in a passive dendritic tree: An analytical investigation.

Modeling electrocortical activity through improved local approximations of integral neural field equations (2007)
Journal Article
Coombes, S., Venkov, N., Shiau, L., Bojak, I., Liley, D., & Laing, C. (2007). Modeling electrocortical activity through improved local approximations of integral neural field equations. Physical Review E, 76(5), https://doi.org/10.1103/PhysRevE.76.051901

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equatio... Read More about Modeling electrocortical activity through improved local approximations of integral neural field equations.

Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities (2007)
Journal Article
Owen, M. R., Laing, C., & Coombes, S. (2007). Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities. New Journal of Physics, 9(378), https://doi.org/10.1088/1367-2630/9/10/378

In this paper we consider instabilities of localised solutions in planar neural field firing rate models of Wilson-Cowan or Amari type. Importantly we show that angular perturbations can destabilise spatially localised solutions. For a scalar model... Read More about Bumps and rings in a two-dimensional neural field: splitting and rotational instabilities.

A bidomain threshold model of propagating calcium waves (2007)
Journal Article
Thul, R., Smith, G., & Coombes, S. (2008). A bidomain threshold model of propagating calcium waves. Journal of Mathematical Biology, 56(4), https://doi.org/10.1007/s00285-007-0123-5

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travell... Read More about A bidomain threshold model of propagating calcium waves.

Dynamic instabilities in scalar neural field equations with space-dependent delays (2007)
Journal Article
Venkov, N., Coombes, S., & Matthews, P. (2007). Dynamic instabilities in scalar neural field equations with space-dependent delays. Physica D: Nonlinear Phenomena, 232(1), 1-15. https://doi.org/10.1016/j.physd.2007.04.011

In this paper we consider a class of scalar integral equations with a form of space-dependent delay. These nonlocal models arise naturally when modelling neural tissue with active axons and passive dendrites. Such systems are known to support a dynam... Read More about Dynamic instabilities in scalar neural field equations with space-dependent delays.

Branching dendrites with resonant membrane: a "sum-over-trips" approach (2007)
Journal Article
Coombes, S., Timofeeva, Y., Svennson, C.-M., Lord, G., Josic, K., Cox, S. J., & Colbert, C. (2007). Branching dendrites with resonant membrane: a "sum-over-trips" approach. Biological Cybernetics, 97(2), https://doi.org/10.1007/s00422-007-0161-5

Dendrites form the major components of neurons. They are complex branching structures that receive and process thousands of synaptic inputs from other neurons. It is well known that dendritic morphology plays an important role in the function of dend... Read More about Branching dendrites with resonant membrane: a "sum-over-trips" approach.

Exotic dynamics in a firing rate model of neural tissue with threshold accommodation (2007)
Journal Article
Coombes, S., & Owen, M. R. (2007). Exotic dynamics in a firing rate model of neural tissue with threshold accommodation. https://doi.org/10.1090/conm/440/08480

Many of the equations describing the dynamics of neural systems are written in terms of firing rate functions, which themselves are often taken to be threshold functions of synaptic activity. Dating back to work by Hill in 1936 it has been recognize... Read More about Exotic dynamics in a firing rate model of neural tissue with threshold accommodation.