Durata: 20 ore


Course title

Periodic orbits of dynamical systems

Number of hours



Mat/08 Numerical Analysis

Lecturers and periods

Dimitri Breda (Udine,, 1st part 1-5 July 2019, 8hrs;

Hinke Osinga (Auckland, 2nd part 9-11 September 2019, 6hrs;

Bern Krauskopf (Auckland, 3rd part 11-13 September 2019, 6hrs.

Learning objectives

It is an advanced course devoted to the study of periodic orbits of continuous-time dynamical systems generated by autonomous ordinary differential equations. The term “advanced” is used not because the specific subject is advanced itself, rather because the concerned arguments hardly find proper room in standard courses at the MSc level. Therefore, the main objective is to provide those interested in dynamical systems with a further step to complete a basic knowledge of the subject of stability beyond the study of equilibria and stationary solutions, the latter being commonly dealt with in traditional courses.


The course focuses on periodic orbits of dynamical systems generated by ordinary differential equations. In the first part we introduce the necessary tools to answer the fundamental question of local stability of these invariants, resorting to the classic theory of Floquet in connection with Poincaré maps. In the second part we address the problem of computing these orbits, as solutions of boundary value problems in the framework of numerical continuation. In the third and last part we deal with the relevant bifurcation analysis under parameter variation, with an eye on specific models and applications.

Teaching methodologies

  • front theoretical lectures;
  • possible laboratory activities on implementation and use of continuation methods;
  • possible seminars on specific arguments.

Learning validation

Certification via seminar/lecture or laboratory activities on a specific argument related to the subject of the course.


  • attendance 4 credits;
  • validation 2 credits.

Other info

  • course offered also to students of the Scuola Superiore, open also to motivated MSc students in mathematics, computer science, engineering or related disciplines;
  • course notes and material provided by the lecturers;
  • prerequisites: standard on differential equations, mathematical and numerical analysis, linear algebra;
  • teaching language: English.


Altro: lingua inglese, corso mutuato dal corso di dottorato.

Elenco corsi 2018/2019