Nonlinear dynamics governs the evolution of a tremendously large number of phenomena in our world. These phenomena are observed in fluid dynamics, biology, mechanical and acoustic vibrations, finance, and many more areas. The beauty of nonlinear dynamics is that it is universal: even if developed or learned in a specific context, the same theory and tools can be then used to understand the nonlinear effects of a completely different, seemingly unrelated subject.
The course aims to (i) explain the foundations of nonlinear dynamical systems in relation to the solution of nonlinear differential equations describing physical systems of relevance for engineering applications, and to (ii) introduce some of the graphical, mathematical and numerical methods used to study and model nonlinear phenomena. Geometric intuition will aid in keeping the mathematical formalism to a minimum. Real-world examples borrowed from state-of-the-art research in various fields, with a focus on engineering, will aid in attracting the student's interest and in demonstrating the usefulness of the thought methods. In this sense, the "teaching by example" approach will be adopted.
Target group
The course is suitable for all students in the fields of engineering and physics, in the late stage of their Bachelor's studies or at the beginning of their Master's studies. However, due to the universality of the theory underlying the study of nonlinear dynamics, also students from different disciplines -- biology, economy, chemistry... -- who have a clear interest in the study of nonlinear phenomena are welcome to join. If a large number of non-engineers will participate, some of the examples/exercises will be borrowed from other disciplines.
Course aim
- Importance of nonlinear effects in physical phenomenon
- Classification of fixed points and bifurcations
- Understanding of bi-stability and triggering
- Drawing and interpreting phase portraits of low-dimensional dynamical systems
- Qualitative understanding of the method of averaging
Credits info: 6 EC
Fee info
EUR 980: 980 EUR for students
EUR 1460: 1460 EUR for working professionals
For more information click "LINK TO ORIGINAL" below.