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**Harvard**

Coombes, S., Schmidt, H., Laing, C., Svanstedt, N. och Wyller, J. (2012) *Waves in Random Neural Media*.

** BibTeX **

@article{

Coombes2012,

author={Coombes, S. and Schmidt, H. and Laing, C. R. and Svanstedt, Nils and Wyller, J. A.},

title={Waves in Random Neural Media},

journal={Discrete and Continuous Dynamical Systems},

issn={1078-0947},

volume={32},

issue={8},

pages={2951-2970},

abstract={Translationally invariant integro-differential equations are a common choice of model in neuroscience for describing the coarse-grained dynamics of cortical tissue. Here we analyse the propagation of travelling wavefronts in models of neural media that incorporate some form of modulation or randomness such that translational invariance is broken. We begin with a study of neural architectures in which there is a periodic modulation of the neuronal connections. Recent techniques from two-scale convergence analysis are used to construct a homogenized model in the limit that the spatial modulation is rapid compared with the scale of the long range connections. For the special case that the neuronal firing rate is a Heaviside we calculate the speed of a travelling homogenized front exactly and find how the wave speed changes as a function of the amplitude of the modulation. For this special case we further show how to obtain more accurate results about wave speed and the conditions for propagation failure by using an interface dynamics approach that circumvents the requirement of fast modulation. Next we turn our attention to forms of disorder that arise via the variation of firing rate properties across the tissue. To model this we draw parameters of the firing rate function from a distribution with prescribed spatial correlations and analyse the corresponding fluctuations in the wave speed. Finally we consider generalisations of the model to incorporate adaptation and stochastic forcing and show how recent numerical techniques developed for stochastic partial differential equations can be used to determine the wave speed by minimising the L-2 norm of a travelling disordered activity profile against a fixed test function.},

year={2012},

keywords={Integro-differential equations, neural field models, homogenization, random media, field-equations, traveling fronts, spiral waves, dynamics, bumps, homogenization, bifurcations, propagation, convergence, systems},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 157450

A1 Coombes, S.

A1 Schmidt, H.

A1 Laing, C. R.

A1 Svanstedt, Nils

A1 Wyller, J. A.

T1 Waves in Random Neural Media

YR 2012

JF Discrete and Continuous Dynamical Systems

SN 1078-0947

VO 32

IS 8

SP 2951

OP 2970

AB Translationally invariant integro-differential equations are a common choice of model in neuroscience for describing the coarse-grained dynamics of cortical tissue. Here we analyse the propagation of travelling wavefronts in models of neural media that incorporate some form of modulation or randomness such that translational invariance is broken. We begin with a study of neural architectures in which there is a periodic modulation of the neuronal connections. Recent techniques from two-scale convergence analysis are used to construct a homogenized model in the limit that the spatial modulation is rapid compared with the scale of the long range connections. For the special case that the neuronal firing rate is a Heaviside we calculate the speed of a travelling homogenized front exactly and find how the wave speed changes as a function of the amplitude of the modulation. For this special case we further show how to obtain more accurate results about wave speed and the conditions for propagation failure by using an interface dynamics approach that circumvents the requirement of fast modulation. Next we turn our attention to forms of disorder that arise via the variation of firing rate properties across the tissue. To model this we draw parameters of the firing rate function from a distribution with prescribed spatial correlations and analyse the corresponding fluctuations in the wave speed. Finally we consider generalisations of the model to incorporate adaptation and stochastic forcing and show how recent numerical techniques developed for stochastic partial differential equations can be used to determine the wave speed by minimising the L-2 norm of a travelling disordered activity profile against a fixed test function.

LA eng

DO 10.3934/dcds.2012.32.2951

LK http://dx.doi.org/10.3934/dcds.2012.32.2951

OL 30