Bifurcation Theory Home Page
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Professor Keener's home page
Math Biology Program
Department of Mathematics
College of Science
University of Utah
Math 6740 - Bifurcation Theory
Time: T,TH 09:10-10:30 am
Place: AEB 360
Because of my travel schedule, we will not meet on 1/17, 19.
Y. A. Kuznetsov, Elements of Applied Bifurcation Theory, third edition, Springer, 2004.
B. Ermentrout, Simulating, Analyzing, and Animating Dynamical Systems, SIAM, 2002.
H. Kielhofer, Bifurcatiion Theory, An Introduction with Applications to Partial Differential Equations, Springer, 2012. edition, Springer, 2004.
W. J. F. Govaerts, Numerical Methods for Bifurcations of Dynamical Equilibria, SIAM, 2000.
R. Howe, Pattern Formtion, An Introduction to Methods, Cambridge University Press, 2006.
D. G. Schaeffer and J. W. Cain, Ordinary Differential Equations,Basics and Beyond, Springer, 2016.
The course will begin with an introduction to computations of bifurcation curves using XPPAUT (and MATCONT). In addition to the topics in the text, we will cover the Lyapunov-Schmidt method, global bifurcation theorems for Sturm-Liouville eigenvalue problems, the global Hopf bifurcation theorem, bifurcations in pde's, the Ginzberg-Landau equation, the Turing instability and bifurcation (pattern formation), bifurcations such as the Taylor-Couette vortices and Benard instabilities (and maybe thermoacoustic engines.)
Delayed logistic map
discretized Bratu's equation
Predator-Prey system w/ Holling II dynamics
The schedule for the projects is as follows:
For more information contact J. Keener, 1-6089