PHYSICS OF COMPLEX SYSTEMS

The course aims to present a broad overview of models and of statistical and numerical techniques for the study and characterization of complex phenomena, of physical, biological and socioeconomic kind.

Lectures and excercises in the classroom

None

Compulsory

Determinism and predictability. Deterministic chaos and sensitivity to initial conditions. Iterative maps and Hamiltonian systems. Lyapunov exponents. Kolmogorov-Sinai entropy. Strange attractors and fractal dimensions. KAM theorem. Chaos and complexity. Emergency, interdependence and self-organization. Examples of complex systems of various kinds: turbulent fluids, financial and economic systems, biological, geological and social systems. Models and numerical techniques for a quantitative study. Generalized Statistics. Superstatistics. Self-organized criticality. Methods of time series analysis. Cellular automata. Agent-based models. Models of opinion dynamics and synchronization. Efficiency of random strategies. Techniques and algorithms for numerical simulations. Complex networks. Random networks, small-world and scale-free. Characterization and main measures of centrality of complex networks.

R.C. Hilborn : Chaos and Nonlinear Dynamics Oxford University Press (1994)

J.C. Sprott: Chaos and Time-series Analysis,, Oxford University Press (2003)

E. Ott: Chaos in Dynamical systems, Cambridge University Press (1993)

F. R. Badii e A. Politi: Complexity, Cambridge University Press (1997)

Y. Bar-Yam: Dynamics of Complex systems, Westview press (1997)

Z. R.N. Mantegna e H.E. Stanley: An introduction to Econophysics, Cambridge University Press (2000)

H. Kantz e T. Schreiber : Nonlinear Time Series Analysis, Cambridge University Press (2000) S.N. Dorogovtsev e J.F.F. Mendes: Evolution of Networks,, Oxford University Press (2003)

L. Barabasi, Network Science, Cambridge University Press (2016)

On Studium

Preparation of a short written dissertation on one of the topics of the programme for a general oral discussion on the main topics presented during the lectures

What is deterministic chaos and what are Lyapunov exponents ?

What is self-organized criticality?

What is the difference between chaos and complexity?

What is synchronization?

Explain the phenomenon of emergence in a complex systems

What is the difference between a random network and a scale-free one or a small world one