Dresden 2006 – scientific programme

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AKSOE: Physik sozio-ökonomischer Systeme

AKSOE 10: Poster Session (posters are expected to be displayed the full day 8:30-18:00)

AKSOE 10.43: Poster

Wednesday, March 29, 2006, 16:00–18:00, P2

Interaction Spaces: a general method to derive differential equations from multi-agent and cellular automata models — •Paolo Giordano, Sergio Albeverio, Denise Andrey, and Alberto Vancheri — USI, via Canavée, Mendrisio, Switzerland

A new kind of model for complex systems (CS) including cellular automata (CA) and multi-agent models (MM), named Interaction Spaces (IS), is proposed. The state of interacting entities are described by continuum variables. The time evolution is defined through a counting process with a given intensity for each type of interaction, and a continuum probability giving the variation of state variables. The intensities depend on the configuration of a suitable set of interacting entities called ’neighbourhood of the interaction’. The use of a continuum state space permits to prove that the time dynamics of extensive state variables fulfil a system of random DE (RDE) using the concept of forward mean derivative (Nelson, Quantum Fluctuations, 1985). We prove that this RDE reduces, for small stochastic fluctuations, to an ODE for the expected values obtainable using a master equation’s approach. The general definition of IS is illustrated using an urban growth model. In this case the counting processes are Poisson distributed and their intensities are defined using fuzzy logic. The extensive use of a CA and MM-like language permits to easily construct a detailed and realistic model of the CS, but IS can also be studied like continuum dynamical systems, including memory effects and random fluctuations. These results permit to guess the possibility to extend Synergetic’s methods to the wide class of CS described by CA or MM. See www.mate.arch.unisi.ch/ACME for references.