Complex and Dynamical Systems

Recommended Prerequisites

Classical Mechanics I.

Teaching Methods

Lectures with exposure of concepts and fundamental theories, and discussion of practical applications of these concepts.
Problem solving classes with typical examples of the subjects under study.

Learning Outcomes

Main importance: Ability to solve problems; General culture in Physics; Mathematical skills to solve problems;

Secondary: Ability to search and use bibliography; Theoretical understanding of physical phenomena; Depth general knowledge in Physics.

Generic skills: Competence in oral and written communication; Computer skills pertaining to the scope of the study; Competence to solve problems; Competence in critical thinking; Competence in independent learning; Adaptability to new situations; creativity; Initiative and entrepreneurial spirit; Quality concerns; Competence to apply in practice the theoretical knowledge.

Work Placement(s)

No

Syllabus

Oscillators harmonic, damped and forced; periodic and chaotic attractors. Point attractors in autonomous systems. Cycles limit in autonomous systems. Periodic attractors in forced oscillators; the Poincaré map. Chaotic attractors in forced oscillators. Stability and bifurcations; Lyapunov stability. Chaotic behavior of uni and two-dimensional maps; the Hénon map. The Lorenz system. Complexity and emergence. Fractals. Applications to physics.

Head Lecturer(s)

João Carlos Lopes Carvalho

Assessment Methods

Final evaluation
Exam: 100.0%

Continuous evaluation
Resolution Problems: 100.0%

Bibliography

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.