Using Mathcad to Solve a Complex Math Problem

[baltimorebest]

Homework Statement

I attached my problem.

Homework Equations

The Attempt at a Solution

I am attempting to use Mathcad to solve this problem using a computer. I have the problem graphed, but I am unsure what it means by " do not plot the initial transient."

For part b, I have several questions. I don't know how to answer any of those questions. I don't know what an attractor is, or how to tell if there is a region where points cannot escape. I tried to look it up, and couldn't figure it out. Like I said, I have the graphs plotted, so I can refer to those if anyone helps me. Thank you.

 

[Filip Larsen]

I am unsure what it means by " do not plot the initial transient."

If the sequence of points is (x_i,y_i) for i = 0, 1, ..., with (x₀,y₀) being the initial state, it simply means that you should not plot the points until the sequence has converged sufficiently close to the attractor so that it will not "show up" on the plot. This of course begs the question of how many points to leave out before start plotting. As a practical method you can select a k and plot the sequence (x_i,y_i) for i > k, and then increase k in case the transient still shows up on the plot.

For part b, I have several questions. I don't know how to answer any of those questions. I don't know what an attractor is, or how to tell if there is a region where points cannot escape. I tried to look it up, and couldn't figure it out. Like I said, I have the graphs plotted, so I can refer to those if anyone helps me. Thank you.

In popular terms, an attractor is the points in phase space that form the "limit" as you plot trajectories for the system near that attractor. An attractor can be a point, a simple closed curve, or like for chaotic systems, a complicated looking fractal structure. The region around the attractor from which all solutions will converge on the attractor is call the region of attraction for the attractor.

You probably need to find a good textbook that explains these concepts in details suited for your level. Perhaps your teacher for this problem can recommend you one, or, if you specify your background, people here will most likely be able to offer some good references.