Modeling and Control in Social Dynamics

Kinetic and hydrodynamic descriptions in social dynamics

Juan Soler

University of Granada

Starting from the framework of kinetic theory of active particles, where individual interactions are based on dynamical systems deduced from first principles or from stochastic game theory, we discuss two of the most challenging problems related to these models: 1) How the domains of influence and interaction of each individual evolve in time and may affect the emerging collective behavior; 2) how the hydrodynamic description leads to different macroscopic models, in which both the hyperbolic and the nonlinear parabolic regimes inherit the emerging properties of the microscopic scale description.