There exists an increasing demand for computing power and performance in real-time embedded systems, as new, more complex customer requirements and function-alities are appearing every day. In order to support these requirements and func-tionalities without breaking the power consumption wall, many embedded systems areswitching from traditional single-core hardware architectures to multi-core architec-tures. Multi-core architectures allow for parallel execution of tasks on the multiplecores. This introduces many benets from the perspective of achievable performance,but in turn introduces major issues when it comes to the timing predictability ofthe real-time embedded system applications deployed on them. The problem arisesfrom unpredictable and potentially unbounded inter-core interferences, which occuras a result of contention for the shared resources, such as the shared system busor shared system memory. This thesis studies the possible application of constraintprogramming as a resource optimization technique for the purpose of creating oineschedules for tasks in real-time embedded system applications executing on a dual-core architecture. The main focus is placed on tightening inter-core data-propagationinterferences, which can result in lower over-all data-propagation delays. A proto-type of an optimization engine, employing constraint programming techniques on ap-plications comprised of tasks structured according to the Phased Execution Model isdeveloped. The prototype is evaluated through several experiments on a large numberof industry inspired intellectual-property free benchmarks. Alongside the experimentsa case study is conducted on an example engine-control application and the resultingschedule is compared to a schedule generated by the Rubus-ICE industrial tool suite.The obtained results show that the proposed method is applicable to a potentially widerange of abstract systems with dierent requirements. The limitations of the methodare also discussed and potential future work is debated based on these results. / <p>Presentation was held over Zoom, due to the COVID-19 situation.</p>

Cette thèse traite de modèles mésoscopiques de cortex appelés champs neuronaux. Les équations des champs neuronaux décrivent l'activité corticale de populations de neurones, ayant des propriétés anatomiques/fonctionnelles communes. Elles ont été introduites dans les années 1950 et portent le nom d'équations de Wilson et Cowan. Mathématiquement, elles consistent en des équations intégro-différentielles avec retards, les retards modélisant les délais de propagation des signaux ainsi que le passage des signaux à travers les synapses et l'arbre dendritique. Dans la première partie, nous rappelons la biologie nécessaire à la compréhension de cette thèse et dérivons les équations principales. Puis, nous étudions ces équations du point de vue des systèmes dynamiques en caractérisant leurs points d'équilibres et la dynamique dans la seconde partie. Dans la troisième partie, nous étudions de façon générale ces équations à retards en donnant des formules pour les diagrammes de bifurcation, en prouvant un théorème de la variété centrale et en calculant les principales formes normales. Nous appliquons tout d'abord ces résultats à des champs neuronaux simples mono-dimensionnels qui permettent une étude détaillée de la dynamique. Enfin, dans la dernière partie, nous appliquons ces différents résultats à trois modèles de cortex visuel. Les deux premiers modèles sont issus de la littérature et décrivent respectivement une hypercolonne, /i.e./ l'élément de base de la première aire visuelle (V1) et un réseau de telles hypercolonnes. Le dernier modèle est un nouveau modèle de V1 qui généralise les deux modèles précédents tout en permettant une étude poussée des effets spécifiques des retards / This thesis deals with mesoscopic models of cortex called neural fields. The neural field equations describe the activity of neuronal populations, with common anatomical / functional properties. They were introduced in the 1950s and are called the equations of Wilson and Cowan. Mathematically, they consist of integro-differential equations with delays, the delays modeling the signal propagation and the passage of signals across synapses and the dendritic tree. In the first part, we recall the biology necessary to understand this thesis and derive the main equations. Then, we study these equations with the theory of dynamical systems by characterizing their equilibrium points and dynamics in the second part. In the third part, we study these delayed equations in general by giving formulas for the bifurcation diagrams, by proving a center manifold theorem, and by calculating the principal normal forms. We apply these results to one-dimensional neural fields which allows a detailed study of the dynamics. Finally, in the last part, we study three models of visual cortex. The first two models are from the literature and describe respectively a hypercolumn, i.e. the basic element of the first visual area (V1) and a network of such hypercolumns. The latest model is a new model of V1 which generalizes the two previous models while allowing a detailed study of specific effects of delays

This thesis deals with mesoscopic models of cortex called neural fields. The neural field equations describe the activity of neuronal populations, with common anatomical / functional properties. They were introduced in the 1950s and are called the equations of Wilson and Cowan. Mathematically, they consist of integro-differential equations with delays, the delays modeling the signal propagation and the passage of signals across synapses and the dendritic tree. In the first part, we recall the biology necessary to understand this thesis and derive the main equations. Then, we study these equations with the theory of dynamical systems by characterizing their equilibrium points and dynamics in the second part. In the third part, we study these delayed equations in general by giving formulas for the bifurcation diagrams, by proving a center manifold theorem, and by calculating the principal normal forms. We apply these results to one-dimensional neural fields which allows a detailed study of the dynamics. Finally, in the last part, we study three models of visual cortex. The first two models are from the literature and describe respectively a hypercolumn, i.e. the basic element of the first visual area (V1) and a network of such hypercolumns. The latest model is a new model of V1 which generalizes the two previous models while allowing a detailed study of specific effects of delays