This paper deals with the kinetic theory modeling crowd dynamics with the aim of showing how the dynamics at the microscale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations are treated by finite difference methods for hyperbolic equations. Some preliminary reasoning toward the modeling of panic conditions is proposed.

This paper proposes a systems theory approach to the modeling of onset and evolution of criminality in a territory. This approach aims at capturing the complexity features of social systems. Complexity is related to the fact that individuals have the ability to develop specific heterogeneously distributed strategies, which depend also on those expressed by the other individuals. The modeling is developed by methods of generalized kinetic theory where interactions and decisional processes are modeled by theoretical tools of stochastic game theory.