Dans cette thèse, nous abordons les problèmes de la transmission et du traitement de l'information par les assemblées de neurones, du point de vue de l'approche inter-disciplinaire des systèmes complexes en nous référant principalement aux formalismes de la théorie de l'information et de la théorie des systèmes dynamiques. Dans ce contexte, nous nous focalisons sur les mécanismes de représentation de l'information sensorielle par les activités neuronales à travers le codage neuronal. Nous explorons la structure de ce code, à plusieurs échelles grâce à l'étude de différents signaux électrophysiologiques issus de populations de neurones (signaux unitaires, LFP et EEG). Sur le plan méthodologique, nous avons implémenté différents indices permettant d'extraire objectivement l'information des activités neuronales, mais également d'en caractériser la dynamique sous-jacente à partir de séries temporelles de taille finie (le taux d'entropie). Nous avons également étudié un indicateur peu utilisé (le taux d'information mutuelle), qui permet de quantifier l'auto-organisation et les relations de couplage entre deux systèmes. Grâce à des approches théoriques et numériques, nous analysons les propriétés caractéristiques de ces indices et proposons leur utilisation dans le cadre de l'étude des systèmes neuronaux. Ce travail permet de caractériser la complexité de différentes activités neuronales associées aux dynamiques de transmission de l'information. / In this thesis, we address the problem of transmission and information processing by neuronal assemblies, in terms of the interdisciplinary approach of complex systems by referring mainly to the formalisms of information theory and dynamical systems. In this context, we focus on the mechanisms underlying sensory information representation by neuronal activity through neural coding. We explore the structure of this code under several scales through the study of different neuronal population electrophysiological signals (singel unit, LFP and EEG). We have implemented various indices in order to extract objectively information from neural activity, but also to characterize the underlying dynamics from finite size time series (the entropy rate). We also defined a new indicator (the mutual information rate), which quantifies self-organization and relations of coupling between two systems. Using theoretical and numerical approaches, we analyze some characteristic properties of these indices and propose their use in the context of the study of neural systems. This work allows us to characterize the complexity of different neuronal activity associated to information transmission dynamics.

O problema de n?corpos é um dos problemas mais importantes em Sistemas Dinâmicos. Nós estudamos o modelo do problema dos três corpos restrito introduzido por Sitnikov. Nesse modelo os corpos primários tem a mesma massa e o terceiro corpo é de massa muito pequena com respeito aos corpos primários. Usando os métodos de Alekseev, nós mostramos a existência de uma ?ferradura de Smale?como um subsistema da dinâmica do terceiro corpo e concluímos ricas conseqüências probabilísticas. Nós também estudamos o problema pelo método de Melnikov / The n?body problem is one of the most important problems in dynamical systems. We study the model introduced by Sitnikov of restricted three body problem. In this model the primaries are of equal mass and the third body is very small with respect to the primaries. Using methods of Alekseev, we show the existence of ?Smale horseshoe?as a subsystem of the dynamic of the third body and conclude rich probabilistic consequences. We also study the same problem by Melnikov?s method

O problema de n?corpos é um dos problemas mais importantes em Sistemas Dinâmicos. Nós estudamos o modelo do problema dos três corpos restrito introduzido por Sitnikov. Nesse modelo os corpos primários tem a mesma massa e o terceiro corpo é de massa muito pequena com respeito aos corpos primários. Usando os métodos de Alekseev, nós mostramos a existência de uma ?ferradura de Smale?como um subsistema da dinâmica do terceiro corpo e concluímos ricas conseqüências probabilísticas. Nós também estudamos o problema pelo método de Melnikov / The n?body problem is one of the most important problems in dynamical systems. We study the model introduced by Sitnikov of restricted three body problem. In this model the primaries are of equal mass and the third body is very small with respect to the primaries. Using methods of Alekseev, we show the existence of ?Smale horseshoe?as a subsystem of the dynamic of the third body and conclude rich probabilistic consequences. We also study the same problem by Melnikov?s method