
pmid: 25288820
pmc: PMC4186256
arXiv: 1405.0736
handle: 11562/973131 , 11583/2715184 , 11392/2186812 , 11571/1286890
pmid: 25288820
pmc: PMC4186256
arXiv: 1405.0736
handle: 11562/973131 , 11583/2715184 , 11392/2186812 , 11571/1286890
The study of formations and dynamics of opinions leading to the so-called opinion consensus is one of the most important areas in mathematical modelling of social sciences. Following the Boltzmann-type control approach recently introduced by the first two authors, we consider a group of opinion leaders who modify their strategy accordingly to an objective functional with the aim of achieving opinion consensus. The main feature of the Boltzmann-type control is that, owing to an instantaneous binary control formulation, it permits the minimization of the cost functional to be embedded into the microscopic leaders’ interactions of the corresponding Boltzmann equation. The related Fokker–Planck asymptotic limits are also derived, which allow one to give explicit expressions of stationary solutions. The results demonstrate the validity of the Boltzmann-type control approach and the capability of the leaders’ control to strategically lead the followers’ opinion.
Physics - Physics and Society, Consensus dynamic, Opinion leader, FOS: Physical sciences, Boltzmann equation; Collective behaviour; Consensus dynamic; Multi-agent systems; Opinion leader; Optimal control;, Physics and Society (physics.soc-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Optimal control, Boltzmann equation, Multi-agent system, Optimization and Control (math.OC), consensus, kinetic equations, model predictive control, opinion formation, optimal control, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, Collective behaviour, Models of societies, social and urban evolution, FOS: Mathematics, Boltzmann equation; Collective behaviour; Consensus dynamic; Multi-agent systems; Opinion leader; Optimal control; Mathematics (all); Engineering (all); Physics and Astronomy (all), Mathematics - Optimization and Control, Adaptation and Self-Organizing Systems (nlin.AO)
Physics - Physics and Society, Consensus dynamic, Opinion leader, FOS: Physical sciences, Boltzmann equation; Collective behaviour; Consensus dynamic; Multi-agent systems; Opinion leader; Optimal control;, Physics and Society (physics.soc-ph), Nonlinear Sciences - Adaptation and Self-Organizing Systems, Optimal control, Boltzmann equation, Multi-agent system, Optimization and Control (math.OC), consensus, kinetic equations, model predictive control, opinion formation, optimal control, Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics, Collective behaviour, Models of societies, social and urban evolution, FOS: Mathematics, Boltzmann equation; Collective behaviour; Consensus dynamic; Multi-agent systems; Opinion leader; Optimal control; Mathematics (all); Engineering (all); Physics and Astronomy (all), Mathematics - Optimization and Control, Adaptation and Self-Organizing Systems (nlin.AO)
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| influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically). | Top 10% | |
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