Introduction to Dynamical Systems with Applications to Biology
LectureThursdays 11-13h Tutorials Friday 13-14h Attention: Lecture starts on Thursday, September 24 The lecturers will communicate the exact lesson times of ONLINE courses.
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
Lernziel
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
Inhalt
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
Skript
Will be provided as needed.
Literatur
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.
Voraussetzungen / Besonderes
Prerequisites: Calculus; a first course in differential equations; basic linear algebra (eigenvalues and eigenvectors). Matlab programming.
Leistungskontrolle
Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Die Leistungskontrolle wird in jeder Session angeboten. Die Repetition ist ohne erneute Belegung der Lerneinheit möglich.
Prüfungsmodus
schriftlich 120 Minuten
Zusatzinformation zum Prüfungsmodus
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)
Hilfsmittel schriftlich
Keine
Diese Angaben können noch zu Semesterbeginn aktualisiert werden; verbindlich sind die Angaben auf dem Prüfungsplan.
Lernmaterialien
Keine öffentlichen Lernmaterialien verfügbar.
Es werden nur die öffentlichen Lernmaterialien aufgeführt.
Gruppen
Keine Informationen zu Gruppen vorhanden.
Einschränkungen
Keine zusätzlichen Belegungseinschränkungen vorhanden.