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636-0118-00L 4 Credits DR , MSC D-BSSE
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Introduction to Dynamical Systems with Applications to Biology

Lecturers & Examiners: Prof. Dr. Mustafa Hani Khammash
VVZ CR n/a

Last Updated: 2026-06-03 00:07:32

Abstract

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

Resources

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.

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 120 minutes
Aids
None
Final examination (60% of course grade)In-class midterm (40% of course grade)

Course Components

Type Title Time & Place Hours
lecture with exercise Introduction to Dynamical Systems with Applications to Biology
Attention: the lecture will start in the second week of the semester.
No time listed 3 h weekly

Offered In