Exploring a Parameter Space In Lab 3.1, we studied a specific two-parameter family of l...

Exploring a Parameter Space

In Lab 3.1, we studied a specific two-parameter family of linear systems. In this lab, we investigate the three-parameter family

The goal is to produce a “picture” of abc-space, indicating the regions where this system has various types of behavior (spiral sinks, repeated eigenvalues, saddles, etc.). Making a representation of three-dimensional space is difficult, so be creative. In your report, you should address the following items:

Your report: Address the items above, paying particular attention to the quality of your representations of the bc-plane and abc-space.

First consider the case where a = 0. Compute the eigenvalues for this case and determine the exact bc-values where this system has certain types of phase portraits, for example, spiral sinks, sources, saddles, etc. Draw an accurate picture of the bcplane, indicating these different regions. Display all types that arise. Also indicate where you find special situations such as repeated or zero eigenvalues.