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636-0118-00L  Introduction to Dynamical Systems with Applications to Biology

SemesterHerbstsemester 2018
DozierendeM. H. Khammash, A. Gupta
Periodizitätjährlich wiederkehrende Veranstaltung

KurzbeschreibungMany 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
LernzielThe 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
InhaltA 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
SkriptWill be provided as needed.
LiteraturStrogatz, 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 / BesonderesPrerequisites: Calculus; a first course in differential equations; basic linear algebra (eigenvalues and eigenvectors). Matlab programming.