Qualitative analysis of a discrete thermostatted kinetic framework modeling complex adaptive systems

Abstract This paper deals with the derivation of a new discrete thermostatted kinetic framework for the modeling of complex adaptive systems subjected to external force fields (nonequilibrium system). Specifically, in order to model nonequilibrium stationary states of the system, the external force field is coupled to a dissipative term (thermostat). The well-posedness of the related Cauchy problem is investigated thus allowing the new discrete thermostatted framework to be suitable for the derivation of specific models and the related computational analysis. Applications to crowd dynamics and future research directions are also discussed within the paper.