The cortex is a complex system, characterized by its dynamics and architecture, which
underlie many functions such as action, perception, learning, language, and cognition. Its …

We survey recent analytical approaches to studying the spatiotemporal dynamics of
continuum neural fields. Neural fields model the large-scale dynamics of spatially structured …

This book aims to provide an introduction to dynamical systems with multiple time scales. As
in any overview book, several topics are covered only quite briefly. My aim was to focus on …

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 …

Spiral waves are a basic feature of excitable systems. Although such waves have been
observed in a variety of biological systems, they have not been observed in the mammalian …

The bistable Swift-Hohenberg equation exhibits multiple stable and unstable spatially
localized states of arbitrary length in the vicinity of the Maxwell point between spatially …

We investigate stationary spatially localized hexagon patterns of the two-dimensional (2D)
Swift–Hohenberg equation in the parameter region where the trivial state and regular …

This is a book on mathematical neuroscience, in which the unifying theme is wavelike
phenomena at multiple spatial and temporal scales. There are already several excellent …

Neural field models are used to study macroscopic spatiotemporal patterns in the cortex.
Their derivation from networks of model neurons normally involves a number of …

In this paper we show how a local inhomogeneous input can stabilize a stationary-pulse
solution in an excitatory neural network. A subsequent reduction of the input amplitude can …