38437 - Dynamic and Systemic Models

Learning outcomes

The course will provide to the students the basic concepts of the deterministic and stochastic dynamical systems in order to built models for physical, biological and social applications. The student acquires some tecqniques for the data statistical analysis and for the validation problem of a model. In particular the student will be able to build simple dynamical models and to analyze their properties using numerical simulations.

Course contents

   Introduction to the dynamical systems: phase flux, maps and differential equations,phase space, the concept of stability, regular
   and chaotic orbits, pametric analysis of the phase space (bifurcations).

   Introduction to the stochastic dynamics: definition of a stochastic process, the Wiener process and the Brownian motion, stochastic
   differential equations, properties of the diffusion processes.

   Introduction to Models: building a model from experimental observations, different tipologies of models, the importance of spatial
   and time resolution (from microsocpic to macrosocpic models), meaning of control parameters, statistical analysis of the experimental
   measures and the numerical simulations, the validation problem.
  
   Mathematical tools for modeling: non linear maps and differential equations, cellular automata and agent based models, networks.
  
   The students are encouraged to develop a simple model related to physical, biological and social applications to apply the theoretical
   aspects discussed along the course.

Readings/Bibliography

Nino Boccara "Modeling Complex Systems" Graduate Text in Contemporary Physics, Springer, 2004 
  

notes of the lecturer

Teaching methods

lessons and analysis of elaborates

Assessment methods

oral exam and discussion of an elaborate

Teaching tools

A programming language as C++ or an enviroment as MathLab will be used to implement a dynamical model

Office hours

See the website of Armando Bazzani