Neural field modelling

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In these five lectures I will describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of spatio-temporal patterns, based around natural extensions of those used for local differential equation models. I present an overview of these techniques, covering Turing instability analysis, amplitude equations, and travelling waves in both homogeneous and heterogeneous models. The last lecture discusses the spiking Lighthouse model of Haken, and advocates this as a tractable model that may allow for the development of an exactly soluble neurodynamics that goes beyond the standard mean field approach. Lecture 1: Tissue level firing rate models with axo-dendritic connections I – Turing instability analysis Lecture 2: Tissue level firing rate models with axo-dendritic connections II – Amplitude equations – Brain wave equations Lecture 3: Travelling waves and localised states – Construction and stability (Evans functions) – Interface dynamics Lecture 4: Waves in random neural media Lecture 5: Tissue level spiking models: the dynamics of the continuum Lighthouse model