CSCI 4446/5446 Course materials
TA help hours will be held on on mondays from 10am-noon in ECCS 114J
starting on 23 January.
General information and administrivia
A version of CSCI 4446/5446 is available through
the Complexity Explorer
MOOC platform housed by the
Santa Fe Institute. We'll be supplementing the on-campus
course with some of these materials this spring. These MOOC materials
may be useful to you in other ways as well, especially if you have to
miss a lecture. Please go to that website, register for the course
(which is called "Nonlinear Dynamics: Mathematical and Computational
Approaches"), and look around a bit, including through the
"supplementary materials" page.
Problem Set 1: logistic map. You can use the logistic map app on
the Complexity Explorer MOOC to check that your solutions are correct
(look in the "supplementary materials" tab). Also, you may wish to
take some time this week to review section 1 of the ODE notes listed
below ("Liz's written notes and videos") if your knowledge of
differential equations is at all rusty.
Problem Set 2: bifurcation diagrams
and Feigenbaum's constant. Again, you can use the Complexity Explorer
logistic map app mentioned above to check your solutions.
Problem Set 3: fractals. For some
examples of fractals in the wild,
click
here or
here.
Final
Project Guidelines: you can find tech reports that compile
projects from some previous
semesters here.
Search for the title "Projects in Chaotic Dynamics..."
Problem Set 4: Runge-Kutta and the driven pendulum equations. You
can download a pdf of the Parker & Chus book in the optional reading
list from the
CU Libraries, but you'll need to be on a campus network (or the
VPN).
Problem Set
5: adaptive Runge-Kutta and the Lorenz and Rossler systems. The
following materials may be useful to you as you do this problem set:
Final Project Details
Problem Set 6: Poincare sections. You can download a pdf of the
Parker & Chus book in the optional reading list from the
CU Libraries, but you'll need to be on a campus network (or the
VPN).
Problem Set
7: variational equation. See the notes listed below ("Liz's
written notes and videos"). Once again, you can download a pdf of the
Parker & Chus book in the optional reading list from the
CU Libraries, but you'll need to be on a campus network (or the
VPN).
Problem Set 8: embedding.
The following materials may be useful to you as you do this problem
set:
Problem Set 9:
Lyapunov exponents.
The following materials may be useful to you as you do this problem
set:
Problem Set 10: fractal dimension.
Click
here for a detailed list of the assigned reading for this topic
and
here for a scan of some of that reading (pp166-191 of Parker
& Chua). You can download a pdf of the whole book from the
CU Libraries, but you'll need to be on a campus network (or the
VPN). Here is
a jpg
of the Hunt & Sullivan proof.
Some hints
about presentations.
Problem Set 11:
playing with bike wheels, writing Lagrangians, and starting to explore
the two-body problem for a binary star. This material is covered in
the first few sections of the classical mechanics notes listed below
("Liz's written notes and videos").
Click
here for a picture defining true anomaly
and here
for a wonderful lecture on dynamical toys like tops and rattlebacks.
Problem Set 12: integrating the two-body equations. See section 4
of the classical mechanics notes listed below. Here's
an interesting
link that Kristine Washburn found about a variant of this problem.
You may also wish to check out the n-body section of Colonna's webpage
(listed below). Here is
the "Chaos
Hits Wall Street" article that's on the reading assignment.
Problem Set 13: integrating the three-body equations for a
binary-field star collision. See section 4.2 of the classical
mechanics notes listed below. The "visualization of dynamical
systems" page in the "interesting links" list below has source code
for a lovely visualization of this problem.
Liz's videos and written materials
The
Complexity
Explorer version of this course. Click on "Lectures" to get to
the course materials.
The
mapping of which videos and quizzes on that website go with which CSCI
4446/5446 lectures
Notes on Taylor series and error in numerical methods (not required,
but possibly useful)
Notes on ordinary differential
equations (ODEs) and solving them numerically
Notes on the variational
equation
A book chapter and a review article about nonlinear
time-series analysis ("TSA Notes")
A schematic of Wolf's algorithm
for computing the largest positive Lyapunov exponent
Notes on classical mechanics
Some useful and/or interesting links: (caveat emptor!)
A
SIAM News piece about numerical dynamics in the solar system that
came out of a final project in this class, also
featured
on the CS Department website.
A great article from Quanta magazine entitled
The
Hidden Heroines of Chaos" about the people who carried out
Lorenz's computer simulations. (There are lots of other "hidden
figures" in this field, including
Lise
Meitner and
Mary Tsingou Menzel).
xkcd's takes on chaos (and
curve-fitting)
A nice
youtube lecture
about fractals (21 min)
An amazing
animated bifurcation diagram
Riding around on the Lorenz
attractor
A
transcript of Lorenz's 1972 speech to
the AAAS entitled "Predictability: Does the flap of a butterfly's
wings in Brazil set off a tornado in Texas?"
Pendulum stuff:
Henri Poincare didn't only play a formative role in the
foundation of the field of nonlinear dynamics. Among other things, he
came up with the theory of relativity and wrote down e=mc^2 before
Einstein did. Read a bit about
him here.
Michael Skirpan's
fractal tree generator (= the mother of all solutions to PS3).
CU's
site license for Matlab now covers student computers!
The
visualization of dynamical systems page from the Nonlinear
Dynamics and Time Series Analysis Group at the Max Planck Institute
for the Physics of Complex Systems.
Video recordings of the lectures from Steve
Strogatz's introductory course on nonlinear dynamics and chaos
Complexity, the flip side of
chaos: complex
dynamics of a flock of starlings. Here's
the Vimeo version of that
video if you prefer that channel.
Movies of metronomes synchronizing (modern-day equivalent of
Huyghens' pendulum clocks): an array of five
and an
array of 32 (!)
The
PhET project, an interactive simulator that you can use to explore
all sorts of interesting systems. Click on "Play with sims" and go to
"Physics" for the n-body simulator (called "My Solar System").
Unfortunately PhET uses Adobe Flash, which has been deprecated. I've
left this link here in case you have a workaround.
Analog computers for nonlinear dynamical systems: the
Antikythera
mechanism and the
digital
orrery (built by Liz's advisor)
"Guide to
Takens' Theorem" paper (heavy going, mathematically, but very
comprehensive).
Rigid body
dynamics in zero gravity on the international space station.
A gorgeous youtube video that zooms in on the
Mandelbrot set.
Another gorgeous video of an
evolving 3D fractal surface.
A 'chalkmation' youtube video - complete with music - about the
Mandelbrot
set (warning: a bit of foul language at the end).
The
TISEAN time-series analysis toolkit.
Chaos in the path of a Roomba
Chaotic music & dance stuff:
NASA's movie of
Hyperion tumbling
Remember that wonderful
"powers of ten" video from high-school physics?
SIAM's dynamics
tutorials, many of which were contributed by grad students in courses
like this one.
Wolfram's Mathworld site.
The
FAQ for sci.nonlinear. A fabulous resource.
The Santa Fe Institute,
which has a couple of
great educational programs for graduate students (the Complex
Systems Summer School) and undergraduates (called "Research
Experiences for Undergraduates").
The Chaos
Hypertextbook
Helwig Hauser's visualization
of dynamical systems page. The pages above that are interesting,
too.
Jean-Francois Colonna's
"virtual space-time travel" page, which includes lots of stuff
about the Lorenz system, pendula, the n-body problem, etc. Very nice
graphics.
Some sources of interesting time series data:
Would you like your own double pendulum?
