**Welcome to** **Nonlinear Differential Equations and Dynamical Systems****Description:** Models for physical systems and engineering designs are often formulated in the mathematical language of systems of differential equations. To analyse the behaviour of such a system, a basic knowledge in the theory of dynamical systems is highly recommended. While linear algebra methods (decomposition of matrices) suffice to understand and even to solve systems of linear differential equations, it is in general impossible to find formulas for the solutions of nonlinear differential equations. Instead, one uses geometry based methods to obtain qualitative information about the behaviour of the solutions. Some of the catch words are: Critical points, equilibria, periodicity, invariant sets and manifolds, stability theory (Lyapunov and Poincaré), perturbations and bifurcations, chaos and attractors.

The course will be based on lectures, exercises, and on computer experiments in computer algebra systems like MAPLE (or interactive web-based solvers). It is addressed to PhD-students interested in physical modelling and stability questions related to dynamical processes. It should be of interest to students within control theory, medical electronics, signal processing, mechanical and civil engineering, physics and mathematics.

Prerequisites: A basic knowledge of mathematics, as obtained through engineering studies at Aalborg University.**Organizer:** Lisbeth Fajstrup, Associate Professor, email: fajstrup@math.aau.dk**Lecturers:** Lisbeth Fajstrup, Associate Professor, Martin Raussen, Associate Professor and Professor Rafael Wisniewski**ECTS:** 3**Time:** November 6th, 8th, 10th, 14th and 16th**Place:** 8th-16th November: Fibigerstræde 1, room: 35 (fib1/35)**Zip code: **9220

**Aalborg**

City:

City:

**Number of seats:**40

**Deadline:**16th of October

**Important information concerning PhD courses**

We have over some time experienced problems with no-show for both project and general courses. It has now reached a point where we are forced to take action. Therefore, the Doctoral School has decided to introduce a no-show fee of DKK 5,000 for each course where the student does not show up. Cancellations are accepted no later than 2 weeks before start of the course. Registered illness is of course an acceptable reason for not showing up on those days. Furthermore, all courses open for registration approximately three months before start. This can hopefully also provide new students a chance to register for courses during the year. We look forward to your registrations.

- Teacher: Lisbeth Fajstrup
- Teacher: Martin Hubert Raussen
- Teacher: Rafal Wisniewski