Thermostatted kinetic models for complex systems under microscopic external fields

Abstract

Complex systems in the life and applied sciences evolve in time as consequence of the microscopic interactions occurring among the elements constituting the system. In real-world systems, the evolution of the system is usually due to both external actions at the macroscopic scale and interactions with the outer environment at the microscopic scale. This paper is concerned with the development and analysis of mathematical frameworks of the thermostatted kinetic theory for active particles for complex systems subjected both by macroscopic and microscopic external fields (open systems). These new classes of equations constitute a background paradigm for the derivation of specific models for self-organized biological aggregations, traffic-like movement, collective behaviors observed in animal and human communities and economical sciences.