MTH 337 Homework #2 due 5pm Thursday, Feb 7

1. Exploration of the dynamical system
	x -> r*x*(1-x/3)
By choosing various r values, see if you can find at least
6 different kinds of asymptotic dynamics in this system.
Make a table listing the r-values and a description of
the dynamics found at each r-value.
Also make a graphical representation of your results,
in which x is on the horizontal axis and r is on the vertical.
(You can choose your initial x's any way you like.)


2. Here is a program to do one million iterations of the
dynamical map x -> 4*x*(1-x/3), in 3 different versions:

Maple
Octave/Matlab
C++

(a) Use the utility "time" to measure how long each
one takes to run: 

time maple speed_test_maple.txt
time octave speed_test_octave.m
g++ -O3 -o speedtest_c++ speed_test_c++.cpp
time ./speedtest_c++

If 1 million is not enough to get good
results or is too many, you may change that number in each.
What are the speed ratios for the 3 implementations?

(b) What do you make of the fact that the final x's are
all different?