Waves, bumps, and patterns in neural field theories

By Stephen Coombes. Biological cybernetics, 2005

479 citations recorded by the source corpus.

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.

Subfields: Cognitive Neuroscience, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/1ce0dbb1e2316eea07f86c6ca283d2c374320b04

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In Cognitive Neuroscience

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields (2008, methodology): “This simple mathematical model can be extended naturally to accommodate multiple populations and cortical sheets, spike frequency adaptation, neuromodulation, slow ionic currents, and more sophisticated forms of synaptic and dendritic processing as described in the review articles [4,54,55].”
Simulations approaching data: cortical slow waves in inferred models of the whole hemisphere of mouse (2021, unknown): “Elliptical kernels are often used in neural field theories to predict wave properties as a function of the connectivity parameters [27, 28]; this is usually referred to as a direct approach, going from parameters to dynamics.”
Macroscopic description for networks of spiking neurons (2015, background): “[16] Stephen Coombes, “Waves, bumps, and patterns in neural field theories,” Biol.”
Spatiotemporal dynamics of continuum neural fields (2012, background): “establishes the existence of nonlinear traveling wave and stationary bump solutions by explicit construction, see sections 3 and 4 and the review [16].”