6533b85dfe1ef96bd12be793
RESEARCH PRODUCT
FROM DISCRETE KINETIC AND STOCHASTIC GAME THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES
Maria Letizia BertottiMarcello Edoardo Delitalasubject
Class (set theory)Partial differential equationDiscretizationField (physics)Dynamical systems theoryApplied Mathematicspopulation modelsMathematical analysisStochastic gameBoltzmann modelsComplex systemnonlinearityModeling and SimulationApplied mathematicsProbability distributiondiscretizationKinetic theoryMathematicsdescription
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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-07-01 | Mathematical Models and Methods in Applied Sciences |