title: Dynamics of neuronal populations: eigenfunction theory; some solvable cases.
abstract: A novel approach to cortical modelling was introduced by Knight and co-workers in 1996. In their presentation cortical dynamics is formulated in terms of interacting populations of neurons, a perspective that is in part motivated by modern cortical imaging. The approach may be regarded as the application of statistical mechanics to neuronal populations, and the simplest exemplar bears a kinship to the Boltzmann equation of kinetic theory. The disarming simplicity of this linear equation hides the complex behaviour it produces. A purpose of this paper is to investigate and reveal its intricacies by treating a series of solvable special cases. In particular we will focus on issues that relate to the spectral analysis of the underlying operators. A fairly thorough treatment is presented for a simple, but still useful example, that has important consequences for more general situations.
authors.affiliation: Laboratory of Applied Mathematics, Mount Sinai School of Medicine, Box 1012, 1 Gustave L Levy Place, New York, NY 10029, USA.
authors.forename: Lawrence
authors.initials: L
authors.lastname: Sirovich
mesh_terms: D002540:Cerebral Cortex / Q000166:cytology* / Q000502:physiology*; D003198:Computer Simulation; D008959:Models, Neurological; D009434:Neural Pathways / Q000502:physiology; D009474:Neurons / Q000502:physiology*