On the modelling of space dynamics in the kinetic theory for active particles

This paper proposes an analysis of the modelling of space dynamics focused on a general class of models of the kinetic theory for active particles in space homogeneity. Various deterministic and stochastic developments are treated and referred to specific applications. These new classes of equations present different aspects of hybrid characteristic coupling deterministic and stochastic structures, as well as continuous and discrete variables, and constitute a background paradigm for the derivation of models whose qualitative properties are analyzed referring to modelling of complex systems in life and applied sciences.