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Dynamique d'un modèle neuronal, synchronisation et complexité

Abstract : The neuron is a point of interest in various scientific domains as a fundamental cell in the nervous system. Some mathematical models describing neuron behaviour exist. When some of these models interact due to coupling functions, the network behaviour can be analyzed as a complex system, . Firstly, this work presents the main mechanisms governing the neuron behaviour in order to understand the different models. Several models are then presented, including the Hindmarsh-Rose one, dating from 1984. The numerical and theoretical study of the asymptotic and transitory dynamics of the forementioned model is then proposed in the second part of this thesis. In the third part, interaction networks are constructed coupling many of these models. These networks are first studied in terms of complete synchronization. Consequently, some properties emerge, some of which are characterized by power laws. Finally, an algorithm of burst synchronization detection is developped.
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Submitted on : Friday, February 19, 2010 - 11:24:44 AM
Last modification on : Friday, April 1, 2022 - 1:40:01 PM
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  • HAL Id : tel-00453912, version 2


Nathalie Corson. Dynamique d'un modèle neuronal, synchronisation et complexité. Mathématiques [math]. Université du Havre, 2009. Français. ⟨tel-00453912v2⟩



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