Evolved neural fields applied to the stability problem of a simple biped walking model
Proceedings of the 11th Annual conference on Genetic and evolutionary computation
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Systematic fluctuation expansion for neural network activity equations
Neural Computation
Intrinsic dendritic filtering gives low-pass power spectra of local field potentials
Journal of Computational Neuroscience
Traveling bumps and their collisions in a two-dimensional neural field
Neural Computation
Hallucinogen persisting perception disorder in neuronal networks with adaptation
Journal of Computational Neuroscience
Hebbian learning of recurrent connections: A geometrical perspective
Neural Computation
Template based black-box optimization of dynamic neural fields
Neural Networks
Journal of Computational Neuroscience
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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.