This two-dimensional map is given by the equations [1,2]

where and .
Note the nonlinear term in the first equation.
Write scripts for iterating with these equations and for making an **x**--**y**
plot of all of the points generated. For sensitivity to initial conditions
(the Butterfly effect), consider the following two cases:

and

and compare the results after 10, 20, 30, 40, and 50 iterations. Next,
perform a large number of iterations (400 or more) and plot the resulting
object. You can see that the general form of the attractor does not depend
on the initial **x** and **y** values, even though the Butterfly effect is
very obvious. What does this exercise tell us about strange attractors?
Examine the behavior of the system for other choices of the constants
and . Are there values of and for which
the attractor disappears?