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Mean field dynamical models over large scale networks
keywords GRAPH, HYDRODYNAMIC LIMIT, INTERACTING AGENTS
Reference persons FABIO FAGNANI
Research Groups Analisi e controllo di sistemi dinamici
Thesis type THEORETICAL AND SIMULATION
Description Socio-economic, financial or infrastructural (electric grids, transportation) networks represent some of the most challenging and exciting multi-disciplinary scientific areas of these decades. They are of large scale, with a complex dynamical behavior emerging from the interconnection of relatively simple units. The presence of nonlinearities and stochastic effects, as well the complexity of the topology of interconnections make their analysis a formidable task and is catalyzing the energies of a large number of scientists with expertise ranging from economics, theoretical engineering, to mathematics and physics.
A successful approach to study such systems is the so-called mean-field approximation. It amounts to assume that each unit interacts with the rest of the network in a homogeneous 'average' way. This leads to an 'Eulerian point of view' analogous to the one undertaken in fluid dynamics: instead of following the evolution of each single unit, we describe the system through the evolution of a probability measure which takes into consideration the fraction of the population sharing a certain state. Moreover, we can perform the so-called hydrodynamic limit wich consists in taking the limit when the number of units N goes to infinity. Goal of this thesis is to study some specific mean field models.
See also http://calvino.polito.it/~fagnani/topics%20PhD.html
Required skills graphs, probability, basic calculus, differential equations, Matlab
Deadline 27/06/2014
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