We refer to social dynamics as collective group dynamics with emergence of self-organization from simple interaction rule of “social type”. Examples include opinion dynamics as in the Hegselmann-Krause model or alignment dynamic as in the Cucker-Smale models. In particular, the interest is on sparse control algorithms to lead a group to consensus. Applications include modeling of animal groups.

Papers:

1. Piccoli, F. Rossi, E. Trelat: Control to flocking of the kinetic Cucker-Smale model, submitted to SIAM Journal on Mathematical Analysis. pdf
2. Caponigro, A. Lai, B. Piccoli: A nonlinear model of opinion formation on the sphere, to appear on Dynamics of Continuous and Discrete Systems A. pdf
3. Caponigro, M. Fornasier, B. Piccoli, E. Trelat: Sparse stabilization and control of alignment models, Mathematical Models and Methods in Applied Sciences, 25 (2015), 521-564. pdf
4. Fornasier, B. Piccoli, F. Rossi: Mean-field sparse optimal control, Philosophical Transaction of Royal Society of London Series A, 372 (2014), 20130400. pdf
5. Caponigro, M. Fornasier, B. Piccoli, E. Trelat: Sparse stabilization and optimal control of the Cucker-Smale model, Mathematics of Control and Related Fields, 3 (2013), 447-466.
6. Piccoli, F. Rossi: Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, Acta Applicandae Mathematicae, 124 (2013), 73-105. pdf
7. Cristiani, P. Frasca, B. Piccoli: Effects of anisotropic interactions on the structure of animal groups, Journal of Mathematical Biology, 62 (2011), 569-588. pdf