Physical systems far from thermo dynamic equilibrium present excitability and irreversibility. The excitability is responsible for the great sensitivity of these systems to external stimuli while the irreversibility is associated with energy dissipation. The thermal fluctuations, inevitable in any real system, arise due to the interaction between many particles of the system. For such systems one of the best approaches is given by the non-equilibrium Statistical Mechanics, since it is virtually impossible an individualized approach of the motion equations. Many works in the current literature use a Gaussian stochastic modeling (without correlations) to represent the fluctuations. However, there is a growing number of studies reporting the occurrence of correlated fluctuations, mainly related to biological systems. In this thesis we investigate the influence of non-Gaussian stochastic distribution on the properties for two representative excitable models. In the first model we study the influence of distribution on the neural dynamics through the stochastic resonance (SR) mechanism. In the second model we approach the ratchet effect (RE) on directed transport of particles. In both systems we use a non-Gaussian power-law distributed noise obtained through a random multiplicative process (RMP). This process allows a fine tuning of the asymptotic power-law decay exponent. The optimization conditions are reported. In particular, we show that the optimization conditions for resonance and directed transport in Brownian ratchets are reached for a finit decay exponent of the stochastic distribution that represents a Strong non-Gaussian character. As non-Gaussian fluctuations occur with great frequency in natural systems, we believe that the non-Gaussian character can optimize the efficiency on the stochastic transport mechanisms in micro and nanoscale. / Fundação de Amparo a Pesquisa do Estado de Alagoas / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Sistemas físicos fora do equilíbrio termo dinâmico apresentam excitabilidade e irreversibilidade. A excitabilidade é responsável pela grande sensibilidade desses sistemas a estímulos externos enquanto a irreversibilidade está asso ciada à dissipação de energia. As flutuações térmicas, inevitáveis em qualquer sistema real, surgem devido à interação entre as inúmeras partículas do meio. Para tais sistemas uma das melhores abordagens é dada pela Mecânica Estatística de não-equilíbrio, uma vez que é praticamente impossível uma abordagem individualizada das equações de movimento. Muitos trabalhos na literatura atual utilizam uma modelagem estocástica gaussiana (sem correlação) para representar as flutuações. No entanto, há um número crescente de trabalhos que relatam a ocorrência de flutuações correlacionadas, principalmente em sistemas biológicos. Nesta tese nós investigamos a influência da distribuição estocástica não-gaussiana sobre as propriedades de dois modelos excitáveis representativos. No primeiro, estudamos a influência da distribuição sobre a dinâmica neural através do mecanismo de ressonância estocástica (RE). No segundo, abordamos o mecanismo do efeito catraca (EC) sobre o transporte direcionado de partículas. Nos dois sistemas utilizamos um ruído colorido não-gaussiano com distribuição tipo lei de potência obtido através de um processo multiplicativo aleatório (PMA). Esse processo permite o ajuste no do expoente de decaimento assintótico da lei de potência. As condições de otimização são relatadas. Em particular, obtivemos que as condições de otimização para a ressonância e para o transporte direcionado em catracas brownianas são atingidas para um valor finito do expoente da distribuição estocástica que representa um caráter fortemente não-gaussiano. Como flutuações não-gaussianas o correm com muita frequência nos sistemas naturais, acreditamos que o caráter não-gaussiano pode otimizar a eficiência dos mecanismos estocásticos de transporte em micro e nanoescala.

Cette thèse présente la réalisation d’un piège optique dans une configuration originale, le piston optique, où le contrôle sur la phase de l’interférence d’un faisceau incident avec sa réflexion sur un miroir permet de réaliser différents types d’expériences. Nous avons d’abord étudié les propriétés thermodynamiques d’une compression progressive du piston qui fait passer la dynamique de la particule piégée d’une région de stabilité vers une région de bistabilité mécanique. Dans le contexte de la résonance stochastique où une force extérieure périodique est appliquée sur cette dynamique bistable, une approche exploitant le facteur de Mandel ainsi qu’une analyse des délais entre les transitions d’états métastables se révèle efficace pour interpréter nos mesures dans différents régimes de forçage. Nous montrons également comment des nanoparticules métalliques peuvent être piégées aisément dans un tel piston optique et nous exploitons notre configuration pour mesurer de faibles effets de forces optiques. Enfin, nous piégeons des nano-objets chiraux uniques et nous montrons comment la configuration de notre piston permet de réaliser des expériences de reconnaissance chirale par polarimétrie différentielle. / This thesis describes the experimental realization of an original optical trap, the optical piston, where controlling the phase of the interference of an incident beam with its reflection on a mirror allows achieving various experiments. We have first looked into the thermodynamics associated with a progressive compression of the piston leading the dynamics of a trapped particle from a region of stability to a region of mechanical bistability. In the context of stochastic resonance where a periodic external force is applied on this bistable dynamics, an approach exploiting the Mandel factor and a time-delay analysis on the hopping events between metastable states have proven efficient in interpreting the different results acquired in different regimes of drive. We have also shown how metallic nanoparticles can be trapped fairly easily in this kind of optical piston and we exploit our configuration to measure weak optical forces. Finally, we trap unique chiral nano-objects and we show how the configuration of our piston allows the realization of chiral recognition experiments by differential polarimetry.

Diese Arbeit behandelt die Asymptotik von Austritts- und Übergangszeiten für gewisse schwach zeitinhomogene Diffusionsprozesse. Darauf basierend wird ein probabilistischer Begriff der stochastischen Resonanz (SR) studiert. Techniken der großen Abweichungen spielen eine zentrale Rolle. Im ersten Teil der Arbeit (Kapitel 1-3) werden Resultate aus der Theorie der großen Abweichungen für zeithomogene Diffusionen rekapituliert. Es werden die klassischen Resultate von Freidlin und Wentzell und Erweiterungen dieser Theorie präsentiert, und es wird an das Kramers''sche Austrittszeitengesetz erinnert. Teil II befasst sich mit dem Phänomen der SR, d.h. mit Periodizitätseigenschaften von Diffusionen. In Kapitel 4 werden physikalische Maße zur Messung der Periodizität diskutiert. Deren Nachteile legen es nahe, einem alternativen, probabilistischen Ansatz zu folgen, der hier behandelt wird. Das 5. Kapitel dient der Herleitung eines gleichmäßigen Prinzips der großen Abweichungen für Diffusionen mit schwach zeitabhängigem, periodischem Drift. Die Gleichmäßigkeit des Prinzips ermöglicht die exakte Bestimmung exponentieller Übergangsraten in Kapitel 6, das die zentralen Ergebnisse des 2. Teils beinhaltet. Hierdurch wird die Maximierung gewisser Übergangswahrscheinlichkeiten ermöglicht, was zum in Kapitel 7 studierten Resonanzbegriff führt. Teil III der Arbeit setzt sich mit der Asymptotik von Austrittszeiten sogenannter selbststabilisierender Diffusionen auseinander. In Kapitel 8 wird der Zusammenhang zwischen interagierenden Teilchensystemen und selbststabilisierenden Diffusionen erläutert und die Existenz- und Eindeutigkeitsfrage behandelt. Das 9. Kapitel dient dem Studium der großen Abweichungen dieser Klasse von Diffusionen. In Kapitel 10 wird das Kramers''sche Austrittszeitengesetz auf selbststabilisierende Diffusionen übertragen, und in Kapitel 11 wird der Einfluß der selbststabilisierenden Komponente auf das Austrittszeitengesetz illustriert. / In this thesis, we study the asymptotic behavior of exit and transition times of certain weakly time inhomogeneous diffusion processes. Based on these asymptotics, a probabilistic notion of stochastic resonance (SR) is investigated. Large deviations techniques play the key role throughout this work. In the first part (Chapters 1-3) we recall the large deviations theory for time homogeneous diffusions. We present the classical results due to Freidlin and Wentzell and extensions thereof, and we remind of Kramers'' exit time law. Part II deals with the phenomenon of stochastic resonance. That is, we study periodicity properties of diffusion processes. In Chapter 4 we explain the paradigm of stochastic resonance and discuss physical notions of measuring periodicity of diffusions. Their drawbacks suggest to follow an alternative probabilistic approach, which is treated in this work. In Chapter 5 we derive a large deviations principle for diffusions subject to a weakly time dependent periodic drift term. The uniformity of the obtained large deviations bounds w.r.t. the system''s parameters plays a key role for the treatment of transition time asymptotics in Chapter 6, which contains the main result of the second part. The exact exponential transition rates obtained here allow for maximizing transition probabilities, which finally leads to the announced probabilistic notion of resonance studied in Chapter 7. In the third part we investigate the exit time asymptotics of a certain class of so-called self-stabilizing diffusions. In Chapter 8 we explain the connection between interacting particle systems and self-stabilizing diffusions, and we address the question of existence. The following Chapter 9 is devoted to the study of the large deviations behavior of these diffusions. In Chapter 10 Kramers'' exit law is carried over to our class of self-stabilizing diffusions. Finally, the influence of self-stabilization is illustrated in Chapter 11.

In dieser Arbeit versuche ich, den neuronalen Code, d. h. die Art und Weise, wie die Nervenzellen des Gehirns Informationen in ihrer Aktivität übertragen und verarbeiten, besser zu verstehen, indem ich die Kodierung von Stimuli in neuronalen Systemen untersuche. Zu diesem Zweck analysiere ich die Veränderungen in der Dynamik von neuronalen Standardmodellen, die im Rahmen der statistischen Physik entwickelt wurden, in Bezug auf Veränder- ungen der Parameter und der Konnektivität bei Vorhandensein bzw. Fehlen eines Reizes. Ich verwende informationstheoretische Maße, um die Fähigkeit neuronaler Populationen, empfangene Informationen durch ihren Output zu übertragen, zu quantifizieren. Die vorgestellten Ergebnisse bauen auf einer Vielzahl früherer Studien über unverbundene und rekurrente neuronale Pop- ulationen auf. Einige dieser Studien heben zwei neuronale Code-Kandidaten hervor, die unterschiedliche Profile der Informationsfilterung aufweisen: einen Integrationscode, der als Tiefpass-Informationsfilter fungiert, und einen Synchroniecode, der als Bandpassfilter fungiert. Das Ziel der vorliegenden Arbeit ist es, die Ergebnisse dieser Studien auf Netzwerke mit einem höheren Konnektivitätsgrad, wie er im Kortex beobachtet wird, auszuweiten. / In this thesis I attempt to better understand the neural code, or the way in which the nerve cells of the brain transmit and process information in their activity, through the investigation of stimulus encoding in neural systems. To this end, I analyze changes in the dynamics of standard neuronal models, de- veloped in the framework of statistical physics, to variations in parameters and connectivity in the presence versus the absence of a stimulus. In conjunction, information theoretical measures are utilized to quantify the ability of neu- ronal populations to transmit received information through their output. The presented results build upon a multitude of previous studies of both uncon- nected and recurrent neural populations. Some of these studies highlight two neural code candidates that have distinct information filtering profiles: an in- tegration code that acts as a low-pass information filter and a synchrony code that acts as a bandpass filter. In the following, synaptic connectivity is added in diverse ways in order to extend results of these studies to networks with a higher level of connectivity, as observed in the cortex.

Στην παρούσα διδακτορική διατριβή μελετούμε αλληλεπιδρώντα ανοικτά κβαντικά συστήματα δύο καταστάσεων και μελετούμε τη συμπεριφορά των κβαντικών τους χαρακτηριστικών παρουσία κλασικού θορύβου. Πιο συγκεκριμένα, μελετούμε το χρόνο αποσύμπλεξης δύο qubits του σιδηρομαγνήτη XY του Heisenberg συναρτήσει της ισχύος κλασικού Gaussian λευκού θορύβου, με δεδομένες όλες τις υπόλοιπες παραμέτρους των συστημάτων. Το βασικό μας αποτέλεσμα είναι ότι όλα τα ενδιαφέροντα φαινόμενα που επάγονται απ’ το θόρυβο, δηλαδή ο στοχαστικός συντονισμός, ο στοχαστικός αντι-συντονισμός και το φαινόμενο της θωράκισης (noise shield), εξαρτώνται άμεσα από την αρχική προετοιμασία του συστήματος των δύο qubits είτε αυτό είναι μόνο του είτε είναι υποσύστημα μιας μεγαλύτερης δομής (αλυσίδας qubits). Επίσης παρατηρούμε ότι η θερμοκρασία του περιβάλλοντος μπορεί να αποτελέσει παράγοντα ελέγχου των ανωτέρω φαινομένων. Παρέχουμε ισχυρές ενδείξεις για την ανάγκη χαρτογράφησης του πίνακα πυκνότητας ενός κβαντικού ανοικτού συστήματος με βάση τα φαινόμενα του θορύβου που μπορεί να επιδείξει / In the current Ph.D. thesis we study interacting open quantum two state systems and study the behavior of their quantum features in the presence of classical noise. More specifically, we study the disentanglement time of two Heisenberg's XY ferromagnetic qubits against the strength of classical Gaussian white noise, with all of the other parameters of the system fixed. Our main result is that all of the interesting noise induced effects, i.e. stochastic resonance, stochastic anti-resonance and the noise shield effect, are directly related to the initial preparation of the system of two qubits whether this is alone, or a subsystem of a larger structure (chain qubits). We also notice that the environmental temperature may be used as a control factor of the above effects. We provide strong evidence for the necessity of mapping the density matrix of a quantum open system according to the noise effects it can present.

Ao passar por uma fina camada magnética uma corrente spin polarizada pode produzir um efeito de torque clássico atuando na camada, sendo capaz de gerar precessão e reversão da magnetização. Esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memórias magnéticas não voláteis e em nano-osciladores de alta frequência, entretanto outras características podem ser exploradas. Em particular, devido ao seu caráter não-linear, torques de spin aplicados em camadas magnéticas podem fornecer condições para aparecimento de caos determinístico e ressonância estocástica. Caos determinístico pode ocorrer em sistemas dinâmicos contínuos que tenham ao menos três graus de liberdade. Nesse caso, mesmo que apenas termos determinísticos sejam considerados, a combinação de termos não-lineares e alta sensibilidade em relação a condições iniciais ou pequenas perturbações pode gerar irregularidade e imprevisibilidade no sistema. Ressonância estocástica é o nome que se dá para fenômenos em que a adição de ruído a um sistema pode melhorar a resposta do mesmo, existindo um nível ótimo de ruído. Esse fenômeno pode ser usado para detecção e amplificação de sinais de baixa intensidade, por exemplo. Aqui analisamos a dinâmica da magnetização da camada livre de junções magnéticas em geometrias do tipo nanopilar, com o estudo dividido em dinâmicas determinísticas e estocásticas. Dentro da análise apenas com termos determinísticos, buscamos verificar comportamentos regulares, irregulares e caóticos, caracterizando o sistema através da geração de diagramas com as fases dinâmicas para diferentes valores de parâmetros. Foram vistas duas geometrias diferentes, sendo que em uma delas foi possível fazer a caracterização completa das fases dinâmicas do sistema. No caso de dinâmicas estocásticas, buscamos explorar efeitos não-lineares e flutuações térmicas, analisando ressonância estocástica e sincronização facilitada por ruído em uma junção túnel magnética, além de estudar as respostas dinâmicas quando há apenas o torque de Slonczewski e quando também está presente o torque tipo campo. Foi possível observar a influência de diversos parâmetros, como a amplitude da corrente aplicada e a frequência de entrada, na resposta magnética e na sincronização de dispositivos estocásticos. Além disso, vimos que com a inclusão do torque tipo campo aparece um possível novo comportamento, similar à ressonância, em alta frequência, ainda não detectado experimentalmente. Esses resultados são importantes pela possibilidade de uso desses dispositivos spintrônicos em transmissão segura de dados, comunicação em alta frequência e em uma nova geração de dispositivos bio-inspirados e eficientes energeticamente. / When passing through a fine magnetic layer a spin polarized electric current may result in a classical torque acting on the layer, being capable of causing magnetization precession and reversal. This effect has been object of numerous researches, specially because of possible applications in non-volatile magnetic memories and high frequency nanooscillators. However, other characteristics can be exploited. In particular, because of its non-linear features, spin torques acting on magnetic layers can generate the conditions for deterministic chaos and stochastic resonance to arise. Deterministic chaos may happen in continuous nonlinear dynamical systems with at least three degrees of freedom. In this case, even if only deterministic terms are considered, the combination of nonlinearities with high sensitivity on initial conditions or small perturbations can produce irregularity and unpredictability in the dynamical behaviour. Stochastic resonance is the phenomenon in which the addition of noise in a system can produce a better output, or system response, existing an optimal noise level. This effect can be used as a way to detect and amplify low intensity signal, for example. In this PhD Thesis we study the magnetization dynamics on the free layer of magnetic junctions in nanopillar geometries. The work is divided into two parts: deterministic and stochastic dynamics. When analysing the deterministic case we tried to characterize regular, irregular and chaotic behaviours, producing dynamical phases diagrams for different system parameters. Two different geometries were analysed, being possible to generate a complete characterization of the dynamical phases in one of them. For the stochastic case we tried to explore nonlinear effects and thermal fluctuations, analysing stochastic resonance and noise-enhanced synchronization in a magnetic tunnel junction and studying the dynamical response when only one spin torque is considered, the Slonczewski torque, and also when a perpendicular torque, the field-like torque, is present. We were able to see the influence of several system parameters, such as the amplitude of the applied electric current and the input frequency, on the system response and on the synchronization of stochastic systems. Also, we noticed that with the inclusion of the field-like torque a possibly new high frequency resonance-like behaviour appears. These results are important because of the possibility of using new spintronic devices for secure data transmission, high frequency communications and on a new generation of bio-inspired devices.

Ao passar por uma fina camada magnética uma corrente spin polarizada pode produzir um efeito de torque clássico atuando na camada, sendo capaz de gerar precessão e reversão da magnetização. Esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memórias magnéticas não voláteis e em nano-osciladores de alta frequência, entretanto outras características podem ser exploradas. Em particular, devido ao seu caráter não-linear, torques de spin aplicados em camadas magnéticas podem fornecer condições para aparecimento de caos determinístico e ressonância estocástica. Caos determinístico pode ocorrer em sistemas dinâmicos contínuos que tenham ao menos três graus de liberdade. Nesse caso, mesmo que apenas termos determinísticos sejam considerados, a combinação de termos não-lineares e alta sensibilidade em relação a condições iniciais ou pequenas perturbações pode gerar irregularidade e imprevisibilidade no sistema. Ressonância estocástica é o nome que se dá para fenômenos em que a adição de ruído a um sistema pode melhorar a resposta do mesmo, existindo um nível ótimo de ruído. Esse fenômeno pode ser usado para detecção e amplificação de sinais de baixa intensidade, por exemplo. Aqui analisamos a dinâmica da magnetização da camada livre de junções magnéticas em geometrias do tipo nanopilar, com o estudo dividido em dinâmicas determinísticas e estocásticas. Dentro da análise apenas com termos determinísticos, buscamos verificar comportamentos regulares, irregulares e caóticos, caracterizando o sistema através da geração de diagramas com as fases dinâmicas para diferentes valores de parâmetros. Foram vistas duas geometrias diferentes, sendo que em uma delas foi possível fazer a caracterização completa das fases dinâmicas do sistema. No caso de dinâmicas estocásticas, buscamos explorar efeitos não-lineares e flutuações térmicas, analisando ressonância estocástica e sincronização facilitada por ruído em uma junção túnel magnética, além de estudar as respostas dinâmicas quando há apenas o torque de Slonczewski e quando também está presente o torque tipo campo. Foi possível observar a influência de diversos parâmetros, como a amplitude da corrente aplicada e a frequência de entrada, na resposta magnética e na sincronização de dispositivos estocásticos. Além disso, vimos que com a inclusão do torque tipo campo aparece um possível novo comportamento, similar à ressonância, em alta frequência, ainda não detectado experimentalmente. Esses resultados são importantes pela possibilidade de uso desses dispositivos spintrônicos em transmissão segura de dados, comunicação em alta frequência e em uma nova geração de dispositivos bio-inspirados e eficientes energeticamente. / When passing through a fine magnetic layer a spin polarized electric current may result in a classical torque acting on the layer, being capable of causing magnetization precession and reversal. This effect has been object of numerous researches, specially because of possible applications in non-volatile magnetic memories and high frequency nanooscillators. However, other characteristics can be exploited. In particular, because of its non-linear features, spin torques acting on magnetic layers can generate the conditions for deterministic chaos and stochastic resonance to arise. Deterministic chaos may happen in continuous nonlinear dynamical systems with at least three degrees of freedom. In this case, even if only deterministic terms are considered, the combination of nonlinearities with high sensitivity on initial conditions or small perturbations can produce irregularity and unpredictability in the dynamical behaviour. Stochastic resonance is the phenomenon in which the addition of noise in a system can produce a better output, or system response, existing an optimal noise level. This effect can be used as a way to detect and amplify low intensity signal, for example. In this PhD Thesis we study the magnetization dynamics on the free layer of magnetic junctions in nanopillar geometries. The work is divided into two parts: deterministic and stochastic dynamics. When analysing the deterministic case we tried to characterize regular, irregular and chaotic behaviours, producing dynamical phases diagrams for different system parameters. Two different geometries were analysed, being possible to generate a complete characterization of the dynamical phases in one of them. For the stochastic case we tried to explore nonlinear effects and thermal fluctuations, analysing stochastic resonance and noise-enhanced synchronization in a magnetic tunnel junction and studying the dynamical response when only one spin torque is considered, the Slonczewski torque, and also when a perpendicular torque, the field-like torque, is present. We were able to see the influence of several system parameters, such as the amplitude of the applied electric current and the input frequency, on the system response and on the synchronization of stochastic systems. Also, we noticed that with the inclusion of the field-like torque a possibly new high frequency resonance-like behaviour appears. These results are important because of the possibility of using new spintronic devices for secure data transmission, high frequency communications and on a new generation of bio-inspired devices.

Ao passar por uma fina camada magnética uma corrente spin polarizada pode produzir um efeito de torque clássico atuando na camada, sendo capaz de gerar precessão e reversão da magnetização. Esse efeito tem sido alvo de inúmeras pesquisas, em especial pela possibilidade de aplicações em memórias magnéticas não voláteis e em nano-osciladores de alta frequência, entretanto outras características podem ser exploradas. Em particular, devido ao seu caráter não-linear, torques de spin aplicados em camadas magnéticas podem fornecer condições para aparecimento de caos determinístico e ressonância estocástica. Caos determinístico pode ocorrer em sistemas dinâmicos contínuos que tenham ao menos três graus de liberdade. Nesse caso, mesmo que apenas termos determinísticos sejam considerados, a combinação de termos não-lineares e alta sensibilidade em relação a condições iniciais ou pequenas perturbações pode gerar irregularidade e imprevisibilidade no sistema. Ressonância estocástica é o nome que se dá para fenômenos em que a adição de ruído a um sistema pode melhorar a resposta do mesmo, existindo um nível ótimo de ruído. Esse fenômeno pode ser usado para detecção e amplificação de sinais de baixa intensidade, por exemplo. Aqui analisamos a dinâmica da magnetização da camada livre de junções magnéticas em geometrias do tipo nanopilar, com o estudo dividido em dinâmicas determinísticas e estocásticas. Dentro da análise apenas com termos determinísticos, buscamos verificar comportamentos regulares, irregulares e caóticos, caracterizando o sistema através da geração de diagramas com as fases dinâmicas para diferentes valores de parâmetros. Foram vistas duas geometrias diferentes, sendo que em uma delas foi possível fazer a caracterização completa das fases dinâmicas do sistema. No caso de dinâmicas estocásticas, buscamos explorar efeitos não-lineares e flutuações térmicas, analisando ressonância estocástica e sincronização facilitada por ruído em uma junção túnel magnética, além de estudar as respostas dinâmicas quando há apenas o torque de Slonczewski e quando também está presente o torque tipo campo. Foi possível observar a influência de diversos parâmetros, como a amplitude da corrente aplicada e a frequência de entrada, na resposta magnética e na sincronização de dispositivos estocásticos. Além disso, vimos que com a inclusão do torque tipo campo aparece um possível novo comportamento, similar à ressonância, em alta frequência, ainda não detectado experimentalmente. Esses resultados são importantes pela possibilidade de uso desses dispositivos spintrônicos em transmissão segura de dados, comunicação em alta frequência e em uma nova geração de dispositivos bio-inspirados e eficientes energeticamente. / When passing through a fine magnetic layer a spin polarized electric current may result in a classical torque acting on the layer, being capable of causing magnetization precession and reversal. This effect has been object of numerous researches, specially because of possible applications in non-volatile magnetic memories and high frequency nanooscillators. However, other characteristics can be exploited. In particular, because of its non-linear features, spin torques acting on magnetic layers can generate the conditions for deterministic chaos and stochastic resonance to arise. Deterministic chaos may happen in continuous nonlinear dynamical systems with at least three degrees of freedom. In this case, even if only deterministic terms are considered, the combination of nonlinearities with high sensitivity on initial conditions or small perturbations can produce irregularity and unpredictability in the dynamical behaviour. Stochastic resonance is the phenomenon in which the addition of noise in a system can produce a better output, or system response, existing an optimal noise level. This effect can be used as a way to detect and amplify low intensity signal, for example. In this PhD Thesis we study the magnetization dynamics on the free layer of magnetic junctions in nanopillar geometries. The work is divided into two parts: deterministic and stochastic dynamics. When analysing the deterministic case we tried to characterize regular, irregular and chaotic behaviours, producing dynamical phases diagrams for different system parameters. Two different geometries were analysed, being possible to generate a complete characterization of the dynamical phases in one of them. For the stochastic case we tried to explore nonlinear effects and thermal fluctuations, analysing stochastic resonance and noise-enhanced synchronization in a magnetic tunnel junction and studying the dynamical response when only one spin torque is considered, the Slonczewski torque, and also when a perpendicular torque, the field-like torque, is present. We were able to see the influence of several system parameters, such as the amplitude of the applied electric current and the input frequency, on the system response and on the synchronization of stochastic systems. Also, we noticed that with the inclusion of the field-like torque a possibly new high frequency resonance-like behaviour appears. These results are important because of the possibility of using new spintronic devices for secure data transmission, high frequency communications and on a new generation of bio-inspired devices.

Dans cette thèse nous avons utilisé des méthodes de systèmes dynamiques et des simulations numériques pour étudier les mécanismes d'oscillations d'épilepsie associés à des concentrations d’ions dynamiques et au comportement bimodal des cellules Purkinje du cervelet. Le propos général de ce travail est l'interaction entre les propriétés intrinsèques des neurones simple et la structure d'entrée synaptique contrôlant l'excitabilité neuronale. Dans la première partie de la thèse nous avons développé un modèle de transition de crise épileptique dans le lobe temporal du cerveau. Plus précisément nous nous sommes concentrés sur le rôle du cotransporteur KCC2, qui est responsable de la maintenance du potassium extracellulaire et du chlorure intracellulaire dans les neurones. Des données expérimentales récentes ont montré que cette molécule est absente dans un groupe significatif de cellules pyramidales dans le tissue neuronal de patients épileptiques suggérant son rôle épileptogène. Nous avons trouvé que l'addition d’une quantité critique de cellules pyramidale KCC2 déficient au réseau de subiculum, avec une connectivité réaliste, peut provoquer la génération d’oscillations pathologiques, similaire aux oscillations enregistrées dans des tranches de cerveau épileptogène humaines. Dans la seconde partie de la thèse, nous avons étudié le rôle du bruit synaptique dans les cellules de Purkinje. Nous avons étudié l'effet de l'inhibition de la génération du potentiel d’action provoquée par injection de courant de bruit, un phénomène connu comme résonance stochastique inverse (RSI). Cet effet a déjà été trouvé dans des modèles neuronaux, et nous avons fournis sa première validation expérimentale. Nous avons trouvé que les cellules de Purkinje dans des tranches de cerveau peuvent être efficacement inhibées par des injectionsde bruit de courant. Cet effet est bien reproduit par le modèle phénoménologique adapté pour différentes cellules. En utilisant des méthodes de la théorie de l'information, nous avons montré que RSI prend en charge une transmission efficace de l'information des cellules de Purkinje simples suggérant son rôle pour les calculs du cervelet. / In this thesis we used dynamical systems methods and numericalsimulations to study the mechanisms of epileptic oscillations associated with ionconcentration changes and cerebellar Purkinje cell bimodal behavior. The general issue in this work is the interplay between single neuron intrinsicproperties and synaptic input structure controlling the neuronal excitability. In the first part of this thesis we focused on the role of the cellular intrinsicproperties, their control over the cellular excitability and their response to thesynaptic inputs. Specifically we asked the question how the cellular changes ininhibitory synaptic function might lead to the pathological neural activity. We developed a model of seizure initiation in temporal lobe epilepsy. Specifically we focused on the role of KCC2 cotransporter that is responsible for maintaining the baseline extracellular potassium and intracellular chloride levels in neurons. Recent experimental data has shown that this cotransporter is absent in the significant group of pyramidal cells in epileptic patients suggesting its epileptogenic role. We found that addition of the critical amount of KCC2-deficient pyramidal cells to the realistic subiculum network can switch the neural activity from normal to epileptic oscillations qualitatively reproducing the activity recorded in human epileptogenic brain slices. In the second part of this thesis we studied how synaptic noise might control the Purkinje cell excitability. We investigated the effect of spike inhibition caused by noise current injection, so-called inverse stochastic resonance (ISR). This effect has been previously found in single neuron models while we provided its first experimental evidence. We found that Purkinje cells in brain slices could be efficiently inhibited by current noise injections. This effect is well reproduced by the phenomenological model fitted for different cells. Using methods of information theory we showed that ISR supports an efficient information transmission of single Purkinje cells suggesting its role for cerebellar computations.

Dans cette thèse, le comportement d'un modèle mathématique permettant de transcrire la dynamique neuronale est étudié : le système de FitzHugh-Nagumo. En particulier, nous nous intéressons au caractère aléatoire d'ouverture et de fermeture des canaux ioniques d'un neurone qui reçoit ou non un stimulus. Ce caractère aléatoire de la dynamique neuronale est considéré, dans notre modèle, comme un bruit. Dans un premier temps, le comportement du modèle de FitzHugh-Nagumo a été caractérisé au voisinage de la bifurcation d'Andronov-Hopf qui traduit la transition entre l'état d'activation et l'état de repos du neurone. Classiquement, un neurone positionné à l'état de repos ne produit aucun potentiel d'action. Cependant, il a été montré un phénomène pour lequel une quantité appropriée de bruit permet la production de potentiels d'action des plus réguliers : la résonance cohérente. Le deuxième effet observé lors de simulations numériques permet au neurone d'améliorer la détection et l'encodage d'un signal subliminal : il s'agit de la résonance stochastique. De plus, cette thèse s'inscrit dans un contexte électronique puisqu'en plus de simuler numériquement le système de FitzHugh-Nagumo, les résultats de simulations ont également été confirmés en réalisant un circuit électronique. En effet, nous avons reproduit la dynamique non linéaire du système de FitzHugh-Nagumo à l'aide de ce circuit électronique. Cela a permis de mettre en évidence expérimentalement les deux phénomènes de résonance cohérente et de résonance stochastique pour lesquelles le bruit peut avoir une influence constructive sur le comportement de notre circuit électronique. / We study the nonlinear FitzHugh-Nagumo model witch describes the dynamics of excitable neural element. It is well known that this system exhibits three different possible responses. Indeed, the system can be mono-stable, oscillatory or bistable. In the oscillatory regime, the system periodically responds by generating action potential. By contrast, in the mono-stable state the system response remains constant after a transient. Under certain conditions, the system can undergo a bifurcation between the stable and the oscillatory regime via the so called Andronov-Hopf bifurcation. In this Phd thesis, we consider the FitzHugh-Nagumo model in the stable state, that is set near the Andronov-Hopf bifurcation. Moreover, we take into account the contribution of noise witch can induces two phenomena coherence resonance and stochastic resonance. First, without external driving, we show the effect of coherence resonance since a critical noise level enhances the regularity of the system response. Another numerical investigation reports how noise can allow to detect a subthreshold deterministic signal applied to the system. In this case, an appropriate amount of noise maximizes the signal to noise ratio reveling the stochastic resonance signature. Besides this numerical studies, we have also built a non linear circuit simulating the FitzHugh-Nagumo model under the presence of noise. This circuit has allowed to confirm experimentally the numerical observation of stochastic resonance and coherence resonance. Therefor, this electronic circuit contributes a framework for further experimental investigation in the field of neural sciences to better understand the role of noise in neural encoding.