11. Phase Plane Analysis

Linearization Intuition — Quiz

Test your understanding of linearization intuition with 5 practice questions.

Practice Questions

Question 1

What is the main goal of linearization near an equilibrium point in a phase plane?

Question 2

For a one-dimensional autonomous equation $x' = f(x)$ with equilibrium at $x^*$, which substitution measures the deviation from equilibrium?

Question 3

In a two-dimensional system with equations $x' = f(x,y)$ and $y' = g(x,y)$, what does the Jacobian matrix contain?

Question 4

If every eigenvalue of the linearized system has $\operatorname{Re}(\lambda) < 0$, how is the equilibrium typically classified?

Question 5

If at least one eigenvalue of the linearized system has $\operatorname{Re}(\lambda) > 0$, what does that usually suggest?