Theoretical aspects of emergence

Emergence refers to the ability of complex systems to spontaneously form large-scale structures which are not directly encoded in the agents' interaction rules.

Complex systems are commonly investigated through microscopic, Agent (or Individual)-Based Models (ABM or IBM), which predict the evolution of each agent in time. When macroscopic models are considered in the literature, they are usually based on phenomenological considerations.This project aims to rigorously establish macroscopic models from their microscopic (Agent-Based Model) counterpart. By doing so, macroscopic models gain in predictive character and may become an invaluable aid for experimental data analysis. ...

Establishing the link between microscopic and macroscopic models is the central task of kinetic theory. However, some of the classical techniques fail due to the specific nature of the agent's interactions in complex systems. Specifically these are:

• the lack of conservation relations, We have overcome this problem by the design of a new concept, that of "generalized collision invariant", which has led us to the derivation of the Self-Organized Hydrodynamic model ,

• the breakdown of propagation of chaos due to the appearance of correlations.

Emergence is the change of state of the system under some parameter changes, i.e. it is a bifurcation (or phase-transition) from a disordered state of the system to an ordered one characterized by some collective behavior. We are specifically interested in three different kinds of phase-transitions:

• symmetry-breaking phase transitions,,

• compressible-incompressible transitions due to volume exclusion,

• continuum-to-network transitions

>>> Back to 'Scientific interests' page