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Duration
Identical coursesAims
Dynamical systems are omnipresent. Therefore, it is desired that students have a thorough understanding of the concepts involved in dynamical systems theory. This course aims at making the students familiar with these concepts and apply them in the analysis of biological systems. Both linear and nonlinear dynamical systems are discussed
Previous knowledge
Matrix algebra, partial derivatives
Prerequisites:
- Linear algebra
- Calculus
If the student has not completed the aforementioned courses, they can be followed in parallel with this course
Is included in these courses of study
Activities
4 ects. Dynamical Systems (B-KUL-I0D48a)
Content
The following items are amply illustrated with concrete examples from various disciplines where possible. Special attention is paid to the application of these concepts for the study of biological systems.
- Introduction: from linear to nonlinear, historic overview and a range of examples.
- Mathematics: revision of some important mathematical concepts which form a basis for the rest of the course like (complex) numbers, functions, operators, Taylor series, differential equations, eigenvalue problems, vectors and matrices.
- Linear system analysis: autonomous systems, continuous vs discrete systems, equilibrium points + characterisation, stability. All these topics are applied to one dimensional and two dimensional systems.
- Nonlinear system analysis: equilibrium points, stability analysis, phase plane and phase portraits, linearisation, bifurcations, chaos.
- Feedback
- Synchronisation
Course material
Course text
Presentation software
Multimedia
Toledo