Ambrogi, Elena
(2021)
Dynamics of an age structured neuron population with the addition of learning processes.
[Laurea magistrale], Università di Bologna, Corso di Studio in
Matematica [LM-DM270]
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Abstract
In this thesis I studied a model which shapes the dynamics of a population of neurons modeled through the time elapsed since their last discharge. The system results in a renewal equation with the addition of the spatial extension and some learning processes. The network is assumed to be non-homogeneous, and the Hebbian learning rule counts for the adaptation of the communication channels between the neurons. In the weak interconnection regime it is proved progressively the well-posedness of the problem, the existence and uniqueness of a stationary solution and the exponential convergence of the system to it. The analysis is conducted both in the linear and non-linear case and makes use of common tools of the mathematical analysis combined with more sophisticated instruments as the Doeblin's theory.
Abstract
In this thesis I studied a model which shapes the dynamics of a population of neurons modeled through the time elapsed since their last discharge. The system results in a renewal equation with the addition of the spatial extension and some learning processes. The network is assumed to be non-homogeneous, and the Hebbian learning rule counts for the adaptation of the communication channels between the neurons. In the weak interconnection regime it is proved progressively the well-posedness of the problem, the existence and uniqueness of a stationary solution and the exponential convergence of the system to it. The analysis is conducted both in the linear and non-linear case and makes use of common tools of the mathematical analysis combined with more sophisticated instruments as the Doeblin's theory.
Tipologia del documento
Tesi di laurea
(Laurea magistrale)
Autore della tesi
Ambrogi, Elena
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum C: Didattico
Ordinamento Cds
DM270
Parole chiave
mathematical analysis neural networks elapsed time renewal equation Hebbian learning rule Doeblin theory
Data di discussione della Tesi
26 Marzo 2021
URI
Altri metadati
Tipologia del documento
Tesi di laurea
(NON SPECIFICATO)
Autore della tesi
Ambrogi, Elena
Relatore della tesi
Scuola
Corso di studio
Indirizzo
Curriculum C: Didattico
Ordinamento Cds
DM270
Parole chiave
mathematical analysis neural networks elapsed time renewal equation Hebbian learning rule Doeblin theory
Data di discussione della Tesi
26 Marzo 2021
URI
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