Multi-active-particle modeling of complex systems within the discrete thermostatted kinetic theory

  • Carlo Bianca Laboratoire Quartz EA 7393, \'{E}cole Sup\'{e}rieure d'Ing\'{e}nieurs en G\'{e}nie \'{E}lectrique, Productique et Management Industriel, 95092 Cergy-Pontoise, France
  • Marco Menale Dipartimento di Matematica e Fisica, Universit\`{a} degli Studi della Campania ``L. Vanvitelli", Viale Lincoln 5, I- 81100 Caserta, Italy


The analysis of a complex system requires the development of suitable mathematical structures able to take into account the multi-agent role. The aim of this paper is the derivation of a preliminary multi-agent framework of the discrete thermostatted kinetic theory for active particles. According to the proposed framework the overal system is divided into primary active particle-subsystems which are subsequently grouped into different functional subsystems composed by active particles sharing the same internal state. The new framework consists into a system of nonlinear ordinary differential equations. The paper is addressed to the existence and uniqueness of the solution of the related Cauchy problem. The main result is obained by employing ODE arguments and $L^1$ estimations. The applications include, but are not limited, to vehicular traffic, crowd dynamics, swarm dynamics, biological, economic, social, and engineering systems.