M.Sc Thesis | |

M.Sc Student | Di Castro Dotan |
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Subject | Population Behavior of Neuronal Networks |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROF. 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.