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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.

Modelling and analysis of planar cell polarity (2008)
Journal Article
Schamberg, S., Houston, P., Monk, N. A., & Owen, M. R. Modelling and analysis of planar cell polarity. Manuscript submitted for publication

Planar cell polarity (PCP) occurs in the epithelia of many animals and can lead to the alignment of hairs, bristles and feathers; physiologically, it can organise ciliary beating. Here we present two approaches to modelling this phenomenon. The aim i... Read More about Modelling and analysis of planar cell polarity.

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.

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

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.

The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study (2006)
Journal Article
Zachariou, M., Dissanayake, D., Owen, M. R., Mason, R., & Coombes, S. The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study. Neurocomputing, 70(10/12), https://doi.org/10.1016/j.neucom.2006.10.065

Gating of sensory (e.g. auditory) information has been demonstrated as a reduction in the auditory-evoked potential responses recorded in the brain of both normal animals and human subjects. Auditory gating is perturbed in schizophrenic patients and... Read More about The role of cannabinoids in the neurobiology of sensory gating: a firing rate model study.

Bumps, breathers, and waves in a neural network with spike frequency adaptation (2005)
Journal Article
Coombes, S., & Owen, M. R. (2005). Bumps, breathers, and waves in a neural network with spike frequency adaptation. Physical Review Letters, 94(14), https://doi.org/10.1103/PhysRevLett.94.148102

In this Letter we introduce a continuum model of neural tissue that include the effects of so-called spike frequency adaptation (SFA). The basic model is an integral equation for synaptic activity that depends upon the non-local network connectivity... Read More about Bumps, breathers, and waves in a neural network with spike frequency adaptation.

Evans functions for integral neural field equations with Heaviside firing rate function (2004)
Journal Article
Coombes, S., & Owen, M. R. Evans functions for integral neural field equations with Heaviside firing rate function. SIAM Journal on Applied Dynamical Systems, 3(4), https://doi.org/10.1137/040605953

In this paper we show how to construct the Evans function for traveling wave solutions of integral neural field equations when the firing rate function is a Heaviside. This allows a discussion of wave stability and bifurcation as a function of syste... Read More about Evans functions for integral neural field equations with Heaviside firing rate function.