Paradigmatic Models in Social Sciences

Politecnico di Milano
May 8 - 10, 2012

Aim of the course
Lecture notes

Last update: Nov 16, 2012

Paradigmatic Models in Social Sciences

Dipartimento di Elettronica e Informazione, Politecnico di Milano
Via Ponzio 34/5, 20133 Milano, Italy

May 8 - 10, 2012

A scientific international course organized by

Department of Electronics and Information (DEI)
Politecnico di Milano

Italian Society for Chaos and Complexity (SICC)


This course is one of the PhD courses supplied by the PhD Program in Information Technology at DEI, Politecnico di Milano. 

The course is addressed to PhD students of the Politecnico di Milano, but also to other PhD students and researchers working in various areas of science and engineering interested in applying dynamical system theory to social sciences.

So far, empirical studies based on experiments and data analysis have dominated the scene in social sciences, while theoretical studies rooted in mathematical models were only exceptions. However, the most recent developments of the theory of dynamical systems, together with the availability of related software, have deeply modified this attitude and generated high expectations around mathematical models. The aim of this course is to show how the scientific approach, traditionally followed in physics and engineering, can be used to tackle social problems. The intent is not to cover specific sectors of social sciences but rather to present and discuss the power of the modelling approach through a series of paradigmatic examples. The examples will be presented in a particular chronological sequence that will allow the main issues of dynamical system theory to be presented in a meaningful order: from bistability to catastrophes, from stationary and cyclic to quasi-periodic and chaotic regimes, from the spreading of successfull strategies to the formation of clusters in networks.

Renato Casagrandi, Department of Electronics and Information, Politecnico di Milano [webpage]
Alessandro Colombo, Department of Electronics and Information, Politecnico di Milano [webpage]
Fabio Dercole, Department of Electronics and Information, Politecnico di Milano [webpage]
Carlo Piccardi, Department of Electronics and Information, Politecnico di Milano [webpage]
Sergio Rinaldi, Department of Electronics and Information, Politecnico di Milano [webpage]
Marten Scheffer, Aquatic Ecology and Water Quality Management group, Wageningen University [webpage]
Karl Sigmund, Faculty for Mathematics, University of Vienna [webpage]
Lucia Tajoli, Department of Management, Economics, and Industrial Engineering, Politecnico di Milano [webpage]

Lecture notes will be made available to the participants at the end of April 2012. They will comprise the PDF of each lecture as well as suggested readings.


Tuesday, May 8
9:00 - 12:30 
Dynamical systems and social sciences
S. Rinaldi Overview of nonlinear dynamics
S. Rinaldi Sexual intercourses in permanent couples
14:00 - 17:30 
Catastrophes and warnings
M. Scheffer Brain, behavior, and social interactions
M. Scheffer Warning signals

Wednesday, May 9
9:00 - 12:30 
Emergence of ups and downs
R. Casagrandi Production in creative professions
S. Rinaldi Political corruption in democratic societies
14:30 - 18:00 
Chaos and unpredictability
F. Dercole Unpredictability of love affairs
A. Colombo Dynamics of two-party democracies

Thursday, May 10
9:00 - 12:30 
Evolutionary games
K. Sigmund Basic principles
K. Sigmund Evolution of cooperation in society
14:00 - 17:30 
Complex networks
C. Piccardi Networks topology
L. Tajoli Evolution of the world trade network


The participation is free of charge but restricted to:

Application is mandatory for all participants:
  • PhD students of Politecnico di Milano must include the course in their study plan, by the usual Poliself procedure;
  • anyone else (e.g., researchers and professors of any Department of Politecnico di Milano, SICC members) must fill in and mail a registration form [click here for the form].
A certificate of attendance will be given to all participants at the end of the course.

Details on exam for Ph.D. students
Unless differently agreed upon with one of the lecturers of the course, the exam will consist of a short (e.g. 5 pages) report (in English) on one of the lectures or on one of the papers suggested as further readings. Typically the report should be organized as follows:

  • Title
  • Abstract (10 lines)
  • Review (long summary of the lecture/paper - 3/4 pages)
  • Comments (criticisms on the content and/or style, suggestions for improvements, possible applications, ... - 1/2 pages)
The report should be send to the organizer of the course ( up to May 2013. The maximum grade will not be given to the reports missing particularly interesting comments.



The course will be held at the Dipartimento di Elettronica e Informazione (DEI), Politecnico di Milano, via Ponzio 34/5, 20133 Milano, in the "Sala Conferenze" (ground floor).

The Department is located in the Bassini campus of Politecnico di Milano. It is at walking distance from the stations Piola and Lambrate FS of the Metro (underground) line 2 ("green line"), as well as from the tram lines 23 and 33, the bus line 93, and the train station Lambrate FS. For further information, you can read these instructions.

The organisers of the course cannot take care of travel and accommodation of the participants. Many hotels are available near the campus [click here for a list], as well as in the center of town [click here for a list].
The Residences and accommodation services of the Politecnico di Milano can also offer a limited number of student accomodations.
For other housing options, see


For enquiries about the course, please contact the organizer Sergio Rinaldi (

PhD students of DEI, please contact the PhD-DEI secretariat ( for any enquiry about the application procedure or any other administrative information. 

Current and prospective SICC members, please contact the SICC secretariat ( for any information.