CS/CogS 3150: Nonlinear Systems
Midterm Review
These review questions are to help you get ready for the midterm.
Be sure to review your notes and the books also . . .
- What is a dynamical system? What are linear and non-linear
dynamical systems? What properties of non-linear systems make
them difficult to analyse?
- What is the logistics equation? Why is it an important
example to study? How is Feigenbaum's Constant related to it?
What is a `period doubling bifurcation cascade'? What universal
properties does the logistics equation reflect? What are the properties
of the system for R > 4? What about for other values of R?
- What is phase space? Breifly discuss, with examples.
- Briefly discuss some differences between continuous and discrete
dynamical systems. Give some examples of each.
- Briefly discuss the oscillator/pendulum/satellite examples. What are
fixed points? What are attractors?
- What are fractals? Why are fractals interesting in the
context of nonlinear systems? Give examples.
- What are the Cantor set, the Mandelbrot set, the Koch snowflake,
the Sierpinski triangle/carpet/sponge? What is a fractal dimension?
How is it calculated? Give an example, and calculate its fractal
dimension.
- What is a fixed point? What is a stable set? What is an attractor?
What is a strange attractor? What is a basin of attraction? What is
a Julia set? What is a limit cycle?
- What are chaotic systems? Why are they resistant to numerical
computation? Why are they worth studying?
- What are some of Poincare's important contributions to the study
of dynamical systems? What is a Poincare section? Who else do you
consider important in the study of nonlinear systems? Why?
- What other interesting/important topics did we discuss? Expand
on at least one.
- Anything else?