Many physical systems are dynamic and are characterized by internal variables that change with time. Describing the quantitative and qualitative features of this change is the topic of dynamical systems theory. Dynamical systems arise naturally in virtually all scientific disciplines including physics, biology, chemistry and engineering. This course is a broad introduction to the topic dynamical s
Objective
The goal of this course is to introduce the student to dynamical systems and to develop a solid understanding of their fundamental properties. The theory will be developed systematically, focusing on analytical methods for low dimensional systems, geometric intuition, and application examples from biology. Computer simulations using matlab will be used to demonstrate various concepts
Content
A dynamical view of the world; the importance of nonlinearity; solutions of differential equations; solving equations on the computer; the phase plane; fixed points and stability; linear stability analysis; classifications of linear systems; Liapunov functions and nonlinear stability; cycles and oscillations; bifurcations and bifurcation diagrams. Many biological examples will be used through the course to demonstrate the concepts
Lecture notes
Will be provided as needed.
Literature
Strogatz, S. H. (2018). Nonlinear dynamics and chaos: with applications to physics, biology, chemistry, and engineering. CRC Press.
Segel, L. A., & Edelstein-Keshet, L. (2013). A Primer in Mathematical Models in Biology (Vol. 129). SIAM.
Prerequisites / Notice
Prerequisites: Calculus; a first course in differential equations; basic linear algebra (eigenvalues and eigenvectors). Matlab programming.
Performance assessment
Performance assessment information (valid until the course unit is held again)
The performance assessment is only offered in the session after the course unit. Repetition only possible after re-enrolling.
Mode of examination
written 120 minutes
Additional information on mode of examination
Final examination (60% of course grade) Homework is compulsory continuous performance assessment of this course and will be assigned regularly and will be graded (40% of course grade)
Written aids
None
This information can be updated until the beginning of the semester; information on the examination timetable is binding.
Learning materials
No public learning materials available.
Only public learning materials are listed.
Groups
No information on groups available.
Restrictions
There are no additional restrictions for the registration.