29 papers found.

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Continuum neural field equations model the large-scale spatio-temporal dynamics of interacting neurons on a cortical surface. They have been extensively studied, both analytically and numerically, on bounded as well as unbounded domains. Neural field models do not require the specification of boundary conditions. Relatively little attention has been paid to the imposition of...

In electrophysiological recordings of the brain, the transition from high amplitude to low amplitude signals are most likely caused by a change in the synchrony of underlying neuronal population firing patterns. Classic examples of such modulations are the strong stimulus-related oscillatory phenomena known as the movement related beta decrease (MRBD) and post-movement beta...

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an \(I_{\text{h}}\) current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory...

The original neural field model of Wilson and Cowan is often interpreted as the averaged behaviour of a network of switch like neural elements with a distribution of switch thresholds, giving rise to the classic sigmoidal population firing-rate function so prevalent in large scale neuronal modelling. In this paper we explore the effects of such threshold noise without recourse to...

The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as predicting novel network states such as chimeras. However, there are many instances where this theory is expected to break down, say in the...

We consider travelling waves (fronts, pulses and periodics) in spatially extended one dimensional neural field models. We demonstrate for an excitatory field with linear adaptation that, in addition to an expected stable pulse solution, a stable anti-pulse can exist. Varying the adaptation strength we unravel the organizing centers of the bifurcation diagram for fronts and pulses...

In this paper, we revisit the work of John G Taylor on neural ‘bubble’ dynamics in two-dimensional neural field models. This builds on original work of Amari in a one-dimensional setting and makes use of the fact that mathematical treatments are much simpler when the firing rate function is chosen to be a Heaviside. In this case, the dynamics of an excited or active region...

Hil GE Meijer
1
**Stephen** **Coombes**
0
0
Center for Mathematical Medicine & Biology, School of Mathematical Sciences, University of Nottingham
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Nottingham, NG7 2RD
,
UK
1
Department of Mathematics

Gap junctions, also referred to as electrical synapses, are expressed along the entire central nervous system and are important in mediating various brain rhythms in both normal and pathological states. These connections can form between the dendritic trees of individual cells. Many dendrites express membrane channels that confer on them a form of sub-threshold resonant dynamics...

At one level of abstraction neural tissue can be regarded as a medium for turning local synaptic activity into output signals that propagate over large distances via axons to generate further synaptic activity that can cause reverberant activity in networks that possess a mixture of excitatory and inhibitory connections. This output is often taken to be a firing rate, and the...

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 advanced, and has allowed for the development of a theory of weakly connected neural networks. However, the strong-attraction...

Neural field models describe the coarse-grained activity of populations of interacting neurons. Because of the laminar structure of real cortical tissue they are often studied in two spatial dimensions, where they are well known to generate rich patterns of spatiotemporal activity. Such patterns have been interpreted in a variety of contexts ranging from the understanding of...

Memories are believed to be represented in the synaptic pathways of vastly interconnected networks of neurons. The plasticity of synapses, that is, their strengthening and weakening depending on neuronal activity, is believed to be the basis of learning and establishing memories. An increasing number of studies indicate that endocannabinoids have a widespread action on brain...

**Stephen** **Coombes**
()
Carlo Laing
0
Institute of Information and Mathematical Sciences, Massey University
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Private Bag 102 904 NSMC, Auckland 0745
,
New Zealand
1
School of Mathematical Sciences

In the study of neurosciences, and of complex biological systems in general, there is frequently a need to fit mathematical models with large numbers of parameters to highly complex datasets. Here we consider algorithms of two different classes, gradient following (GF) methods and evolutionary algorithms (EA) and examine their performance in fitting a 9-parameter model of a...