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.

Describe the behavior of the system for 0 < a < 1.