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Heterogeneity, minorities and leaders in opinion formation
keywords GRAPH, INTERACTING AGENTS, OPINION DYNAMICS
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.
Most of the dynamical systems over networks investigated in the literature assume all the units to be identical: to be endowed with the same endogeneous dynamics and to react in the same way to the network interactions. This is clearly not realistic in many applicative context, particularly in opinion dynamics. More concretely, assume we are modeling the dynamics over a network through a Markov chain describing the possible transitions of the state of a unit in response to the interaction with her neighbors. Heterogeneity implies that this Markov chain is not reversible: this makes the analysis quite difficult when the number of agents is large.
An instance of heterogeneity is the presence of a minority of units behaving in a different way than the majority. This difference may consist in a different endogenous dynamics or in a different capability to interact with the others, and may model conservative or antisocial attitudes. Typical issues to be investigated are the extent to which the minority can condition the over-all system depending on their size, their location in the network, the type of dynamics involved. We expect threshold phenomena to incur in the large scale limit.
Another instance of heterogeneity is the presence of unit leaders influencing the network but not modifying their internal state in the interactions with other units (also called 'stubborn' agents for this reason). The asymptotic behavior of the system clearly depends on the position of the leaders in the network. Important instances to be analyzed are situations where we face the presence of a number of highly connected communities each having their own leaders. Depending on the strength of interaction among the communities we will assist to 'consensus' type state configurations or rather to segregative behaviors. Goal of this thesis is to focus on some specific model and undergo a theoretical and simulative analysis.
See also http://calvino.polito.it/~fagnani/topics%20PhD.html
Required skills graphs, probability, basic calculus, differential equations, Matlab
Deadline 28/06/2014
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