This semester we will study nonlinear dynamics under the influence of time delay.
This course concerns itself with the the theory of delay differential equations and will offer a glimpse of the many fascinating phenomena that can precipitate in an infinite-dimensional phase space. Time delay appears as an intrinsic component of many systems, e.g., signal propagation in optical systems, biological systems with memory effects, complex economic models, and social or ecological networks. Time delay can also be artificially implemented into a system to control its behavior.
Prerequisites are a good knowledge of ordinary differential equations (such as the lecture Dynamical Systems 1 which took place in Summer 2018).
K.T. Alligood, T.D. Sauer and J.A. Yorke: Chaos, Springer, 1997.
H. Amann: Ordinary Differential Equations, de Gruyter, 1990.
V.I. Arnold: Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1988.
W.E. Boyce and R.C. DiPrima: Elementary Differential Equations and Boundary Value Problems, Wiley, 5th edition, 1992.
S.-N. Chow and J.K. Hale: Methods of Bifurcation Theory, Springer, 1982.
E.A. Coddington and N. Levinson: Theory of ordinary differential equations, McGill-Hill, 1955.
P. Collet and J.-P. Eckmann: Concepts and Results in Chaotic Dynamics. A Short Course, Springer, 2006.
R. Devaney, M.W. Hirsch and S. Smale: Differential Equations, Dynamical Systems, and an Introduction to Chaos, Academic Press, 2003.
(This is the updated version of
M.W. Hirsch and S. Smale: Differential Equations, Dynamical Systems, and Linear Algebra, Academic Press, 1974.)
Dynamical Systems I, D.K. Anosov and V.I. Arnold (eds.), Encyclopaedia of Mathematical Sciences Vol 1, Springer, 1988.
J. Hale: Ordinary Differential Equations, Wiley, 1969.
B. Hasselblatt, A. Katok: A First Course in Dynamics, Cambridge 2003.
P. Hartmann: Ordinary Differential Equations, Wiley, 1964.
A. Katok, B. Hasselblatt: Introduction to the Modern Theory of Dynamical Systems, Cambridge 1997.
F. Verhulst: Nonlinear Differential Equations and Dynamical Systems, Springer, 1996.
A3/SR 130 Seminarraum (Hinterhaus)
wöchentlich, ab 09.04.2019, 10:00 - 12:00 (14 Termine)