Neuroscience: Towards a Kinetic Theory of Cortical-like Neural Fields

Neuroscience: Towards a Kinetic Theory of Cortical-like Neural Fields

The kinetic theory of neural fields is based fundamentally on the description of electrical properties of single neurons and on some statistical hypotheses about their connecting network. This chapter discusses the basis of this theory and its main results. It discusses a basilar, minimal set of biological neural features, except those linked to neural plasticity. Such characteristics are utilized for the construction, through statistical-physics methods, of a general mathematical model, which does not refer to particular brain regions. The chapter discusses some results of the application of the theory to cortical-like neural fields and to attention and learning. Neural systems are considered as finite regions of the three-dimensional space filled with two different types of particles. Neurons, characterized by an inner excitation corresponding to the subthreshold membrane potential, constitute a kind of motionless, solid background. They, under some conditions, emit impulses in space.