TY - JOUR

T1 - From Discrete Kinetic and Stochastic Game Theory to Modelling Complex Systems in Applied Sciences

AU - Bertotti, Maria Letizia

PY - 2004

Y1 - 2004

N2 - This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of social dynamics. The derivation of the evolution equation needs the development of a stochastic game theory.

AB - This paper deals with some methodological aspects related to the discretization of a class of integro-differential equations modelling the evolution of the probability distribution over the microscopic state of a large system of interacting individuals. The microscopic state includes both mechanical and socio-biological variables. The discretization of the microscopic state generates a class of dynamical systems defining the evolution of the densities of the discretized state. In general, this yields a system of partial differential equations replacing the continuous integro-differential equation. As an example, a specific application is discussed, which refers to modelling in the field of social dynamics. The derivation of the evolution equation needs the development of a stochastic game theory.

UR - http://hdl.handle.net/10447/2473

UR - https://www.worldscientific.com/doi/pdf/10.1142/S0218202504003544

M3 - Article

VL - 14

SP - 1061

EP - 1084

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

ER -