Neural Fields: Theory and Applications
Stephen Coombes, Peter beim Graben, Roland Potthast, James Wright
Springer, Jun 17, 2014 - Mathematics - 487 pages
Neural field theory has a long-standing tradition in the mathematical and computational neurosciences. Beginning almost 50 years ago with seminal work by Griffiths and culminating in the 1970ties with the models of Wilson and Cowan, Nunez and Amari, this important research area experienced a renaissance during the 1990ties by the groups of Ermentrout, Robinson, Bressloff, Wright and Haken. Since then, much progress has been made in both, the development of mathematical and numerical techniques and in physiological refinement und understanding. In contrast to large-scale neural network models described by huge connectivity matrices that are computationally expensive in numerical simulations, neural field models described by connectivity kernels allow for analytical treatment by means of methods from functional analysis. Thus, a number of rigorous results on the existence of bump and wave solutions or on inverse kernel construction problems are nowadays available. Moreover, neural fields provide an important interface for the coupling of neural activity to experimentally observable data, such as the electroencephalogram (EEG) or functional magnetic resonance imaging (fMRI). And finally, neural fields over rather abstract feature spaces, also called dynamic fields, found successful applications in the cognitive sciences and in robotics. Up to now, research results in neural field theory have been disseminated across a number of distinct journals from mathematics, computational neuroscience, biophysics, cognitive science and others. There is no comprehensive collection of results or reviews available yet. With our proposed book Neural Field Theory, we aim at filling this gap in the market. We received consent from some of the leading scientists in the field, who are willing to write contributions for the book, among them are two of the founding-fathers of neural field theory: Shun-ichi Amari and Jack Cowan.
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ˇ ˇ action activity alpha band alpha rhythm Amari amplitude analysis attractor axonal behavior Biol brain Bressloff cells cognitive Comput connection function Connectome Coombes correlations cortical coupled Cybern dendritic denotes differential equations diffusion distribution domain dynamic field eigenvalues electroencephalographic equilibrium Ermentrout excitation extracellular firing rate function fluctuations Fourier transform frequency GABAA receptor Heaviside homogeneous Hopf bifurcation inhibition inhomogeneous input instability integral interactions inverse Jirsa kernel layer Liley linear macrocolumn master equation motor neural field equation neural field models neural field theory neural mass neural network neurons Neurosci noise nonlinear numerical oscillations parameters patterns peak perturbations Phys physiological population postsynaptic potential propagation propofol pulses pyramidal cells region representation robot saccade SIAM simulation solutions space spatial spatiotemporal speed spike stable stationary bump stimulus stochastic synaptic Syst threshold traveling bumps traveling waves Turing vector visual cortex zero