23762 - Physics of Complex Systems

Learning outcomes

At the end of the class, the student will learn a basic knowledge of Complex Systems Physiscs with application to biological and social systems, and theoretical tools to analyze, to predict and to control the evolution of models.

Course contents

Definition of Complex Systems: a physicist point of view. Statistical Physics and Dynamical System Theory of Complex Systems, scaling laws and their meaning for biological, social and economics systems, the concept of robustness and frailty in a model and phase transition for complex systems. Study of some models for complex systems.

Dynamics systems on network structures: transport and traffic models, neural networks and economics models. Properties
of linear and nonlinear random walks on graphs. Markov models, Master equation and properties of the stationary solutions.

Introduction to stochastic thermodynamics, the concept of Entropy and its applications to equilibrium states and non equilibrium states for a system, information entropy and Gibbs Entropy. Maximal Entropy Principle and detailed balance for Markovian systems. The characterization of stationary equilibrium and non equilibrium states, with examples.

Stochastic dynamical systems as model for complex systems: Critical points and phase transition concept. Nonlinear stochastic models, Kramer's theory for the transition rates, adaptive models and self-consitent stationary states, the concept of self-organized criticality and application to stochastic models on networks.

Readings/Bibliography

Boccara, Nino 'Modeling Complex Systems' Springer (2010)

Yaneer Bar-yam 'Dynamics of Complex Systems' The Advanced Book Studies in Nonlinearity series (1997)

Balescu, R. 'Equilibrium and nonequilibrium statistical mechanics' New York, Wiley-Interscience, 1975. 756 p.

Notes from the teacher

Teaching methods

ex cathedra lessons

Assessment methods

oral examination and discussion of a model chosen by the student

Teaching tools

simulations using a personal computer

Links to further information

http://www.physycom.unibo.it/pagina_web_bazzani.html/bazzani_web_dir/sistemi_complessi/

Office hours

See the website of Armando Bazzani