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A mean field model for movement induced changes in the beta rhythm

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 rebound ...

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex

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 ...

Neural Field Models with Threshold Noise

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 ...

Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience

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 presence ...

Travelling waves in models of neural tissue: from localised structures to periodic waves

Hil GE Meijer 0 Stephen Coombes 0 Department of Applied Mathematics, MIRA Institute of Biomedical Technology and Technical Medicine, University of Twente , Postbus 217, 7500 AE, Enschede, The

Neural ‘Bubble’ Dynamics Revisited

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, ...

Numerical continuation of travelling waves and pulses in neural fields

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

Gap Junctions, Dendrites and Resonances: A Recipe for Tuning Network Dynamics

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. ...

Travelling waves in a neural field model with refractoriness

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 ...

Interface dynamics in planar neural field models

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 visual ...

A Biophysical Model of Endocannabinoid-Mediated Short Term Depression in Hippocampal Inhibition

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 ...

Delays in activity-based neural networks

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

Using Evolutionary Algorithms for Fitting High-Dimensional Models to Neuronal Data

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 ...

Dynamics of activity fronts in a continuum mean field model of cortex

Helmut Schmidt 1 Ingo Bojak 0 Stephen Coombes 1 0 Donders Institute for Brain , Cognition and Behaviour , Centre for Neuroscience, Radboud University Nijmegen (Medical Centre) , P.O. Box 9101 // 126

Limitations of perturbative techniques in the analysis of rhythms and oscillations

Perturbation theory is an important tool in the analysis of oscillators and their response to external stimuli. It is predicated on the assumption that the perturbations in question are “sufficiently weak”, an assumption that is not always valid when perturbative methods are applied. In this paper, we identify a number of concrete dynamical scenarios in which a standard ...