Sistemas Dinâmicos e Complexos - F

Ano letivo: 2010-2011
Specification sheet

Specific details
course codecycle os studiesacademic semestercredits ECTSteaching language

Learning goals

Main importance:

Ability to solve problems.

General culture in Physics.

Mathematical competences to solve problems.


Secondary importance:

Ability to search and use bibliography.

Theoretical understanding of the physical phenomenon.

Thorough general culture in Physics.


Cushioned and forced Harmonic Oscillators; periodic and chaotic attractors.

Isolated attractors in autonomous systems.

Limit cycles in autonomous systems.

Periodic attractors in forced oscillators; the Poincaré map.

Chaotic attractors in forced oscillators.

Stability and bifurcations; Lyapunov stability.

Chaotic behaviour of uni- and bidimensional maps; the Hénon map.

The Lorenz system.

Complexity and emergency. Fractals.

Applications to Physics.


Mathematical Analysis I, II, III.

Linear Algebra and Analytical Geometry.

Computers and Programming.

Classic Mechanics I.

Generic skills to reach
. Computer Skills for the scope of the study;
. Competence to solve problems;
. Competence in autonomous learning;
. Adaptability to new situations;
. Competence in applying theoretical knowledge in practice;
. Competence in oral and written communication;
. Critical thinking;
. Creativity;
. Initiative and entrepreneurial spirit;
. Quality concerns;
(by decreasing order of importance)
Teaching hours per semester
theory-practical classes15
total of teaching hours60

Problem solving100 %
assessment implementation in 20102011
Problems solving and mini-tests : 100.0%

Bibliography of reference

Steven H. Strogatz, (1994) Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, and Engineering, Perseus Book.

JOSÉ, J. V. and SALETAN, E. J. (1998). Classical Dynamics: a contemporary approach. Cambridge: Cambridge University Press.

THOMPSON, J. M. T.; and STEWART, H. B. (2002).  Nonlinear Dynamics and Chaos, Chichester: John Wiley & Sons.

Teaching method

The essential objectives of this curricular unit are those marked with the number1 in the Dublin descriptors mentioned above. The adopted strategy comprises the brief theoretical lecturing of a wide number of topics and an assessment system based on the accomplishment of small project assignments and their reports and 2 mini-tests. These assignments will allow students to thoroughly study some of the systems that are described in theoretical classes. Students will be advised to carry out 4 assignments: the first two should be done during two weeks (the time given to students to accomplish the assignment, which is counted from the day on which the assignment is delivered by the teacher); the last two should be done during 4 weeks. These assignments allow students to develop their ability to do research and their ability to work alone in the resolution of advanced problems.

Resources used
Laboratório de Computação Avançada