. "Modeling complex systems"@en . . "6" . "General introduction about linear versus nonlinear dynamics.\r\nDynamical systems with one variable.\r\nBifurcations in one variable systems: saddle-node, cusp, transcritical and imperfect bifurcations.\r\nBifurcations on the circle, synchronisation.\r\nLinear dynamics with two variables: classification of the fixed points (saddle, node, center, degenerate).\r\nNonlinear dynamics with two variables: phase space analysis, reversibility, Lyapunov function, theory of the index.\r\nLimit cycles: relaxation oscillations, singular perturbation.\r\nChaos: Lorentz model and analysis.\r\nOne dimensional maps: bifurcations, period doubling and intermittency route to chaos, universality.\r\nFractals: self-similarity, fractal dimension.\r\nStrange attractors: stretching and folding, baker’s map, Henon map.\r\nPattern formation.\nALGEMENE COMPETENTIES\r\nThe overall objective of this course is to be able to analyze dynamical systems using geometrical methods on the phase space. This includes carrying out linear stability, bifurcation and phase plane analyses. We will first focus on one and two dimensional systems. Chaotic phenomena in physical systems will be described with two classical examples: the Lorentz strange attractor and the logistic map. Solving problems and reading literature related to the course material is also foreseen." . . "Presential"@en . "FALSE" . . "Others"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Master of Science in Physics and Astronomy"@en . . "https://images.communicate.vub.ac.be/Web/VUB/%7Be03fbc44-87f1-488a-badd-e287777c0353%7D_WE_oplBrochure_MB_EN_Physics-Astronomy_8P.pdf?utm_medium=email&utm_source=eloqua&utm_content=MARCOM%20REKRUTERING%20brochure%20download%20ENG&%3Cutm_campaign= https://www.vub.be/en/studying-vub/all-study-programmes-vub/bachelors-and-masters-programmes-vub/master-in-physics-and-astronomy/program/master/master-physics-and-astronomy-minor-research\n" . "120"^^ . "Presential"@en . "The Master of Science in Physics and Astronomy: Minor Research is composed of 30 ECTS compulsory courses, 30 ECTS master thesis, 10-12 ECTS external mobility courses and 48-50 ECTS minor Research Electives. Our Master is jointly organized with UGent.\n\nPhysics aims at understanding the world around us by observing it from the smallest scales to the scale of the universe itself. From those observations, models are built to allow us to understand, explain and eventually predict the behavior of nature. The Master in Physics and Astronomy provides a comprehensive education in physics covering the particle physics, general relativity, astrophysics and the study of complex systems.\n\nThis master will give you quantitative and analytic skills that are useful to solve many problems arising in many areas beyond physics."@en . . . "2"@en . "TRUE" . . "Master"@en . "Thesis" . "1092.10" . "Euro"@en . "3620.00" . "Recommended" . "As a physicist you will be in high demand on the job market. With a master in Physics and Astronomy from VUB, you will have the knowledge and skills to land a job in one of many diverse sectors.\n\nThere is plenty of work in scientific research at universities and research institutes. In industry, in modelling, statistics and informatics. Alternatively, work on risk analysis and modelling in the banking, finance or pharmaceuticals sectors. You will also be valuable in the field of education. Infinite opportunities, in fact!"@en . "2"^^ . "TRUE" . "Upstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .