|M.Sc Student||Di Castro Dotan|
|Subject||Population Behavior of Neuronal Networks|
|Department||Department of Electrical Engineering||Supervisor||Professor Ron Meir|
|Full Thesis text|
We introduce some new methods for mathematically analyzing the behavior of populations of biologically based neurons. The behavior of large populations of such neurons, provides a fundamental level at which one can describe complex neuronal systems, going beyond single neuron dynamics. Because the nature of large systems is hard to describe explicitly, a statistical analysis is called for, in the spirit of statistical physics. Starting from a description of a large population of stochastic interacting neurons, we describe the ensemble behavior in a mean field setting, based on the so-called Fokker-Planck partial differential equation. The solution to this
(quasi-linear) equation is given analytically in some limiting cases, and numerically in general. The solution provides a characterization of the system under a range of different conditions, depending on the intrinsic network parameters such as excitation/inhibition ratio, connectivity and adaptation level.