TU Berlin

Dynamical Systems and ApplicationsDifferential Equations with Time-Delays

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Lecturers

Lectures: Prof. Serhiy Yanchuk

Exercises: Stefan Ruschel

Differential Equations with Time-Delays

Delay differential equations (or functional differential equations) describe systems, in which time evolution can depend not only on the present state but also on the past. These equations are widely used in many fields such as laser physics, biological models, population dynamics, epidemiology, etc. For instance, the accurate accounting of the signal propagation times in neural networks leads often to time delays.

In this lecture, basic examples and properties of such systems will be given. In particular, we discuss initial value problems, practical methods for solving such systems (method of steps, numerical methods), stability (characteristic quasipolynomial) and shortly the bifurcations.

Link im Vorlesungsverzeichnis

Time and Place

Lecture (Vorlesung): MA645;  Do: 12:00 - 14:00

Exercise (Übung): MA645; Mo: 10:00 - 12:00

(24.04.2017 bis 17.07.2017)

Literature

Hale, J. K. & Lunel, S. M. V. Introduction to Functional Differential Equations
Springer-Verlag, 1993, 447

Smith, H. L. An introduction to delay differential equations with applications to the life sciences Springer, 2010, 57

S. Yanchuk & G. Giacomelli. Topical Review: Spatio-temporal phenomena in complex systems with time delays, J. Phys. A: Mathematical and Theoretical, 2016

Hausaufgaben (Assignments)

  • Sheet 1 - submission deadline: April 26
  • Sheet 2 - submission deadline: May 8
  • Sheet 3 - submission deadline: May 15
  • Sheet 4 - submission deadline: May 22
  • Sheet 5 - submission deadline: May 29
  • Sheet 6 - submission deadline: June 12
  • Sheet 7 - submission deadline: June 19
  • Sheet 8 - submission deadline: June 26
  • Sheet 9 - submission deadline: July 3
  • Sheet 10 - submission deadline: July 10

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