MediumCalculusca-130

Phase Portrait Stability

Problem

For a 2D linear system x' = A*x with trace T and determinant D, the origin is classified by these invariants.

Return "saddle" when D < 0, "stable" when D > 0 and T < 0, "unstable" when D > 0 and T > 0, and "center" when D > 0 and T == 0. When D == 0, return "degenerate".

Hint

The eigenvalues are the roots of lambda^2 - T*lambda + D, and their signs decide stability.

Test cases

case 1

in: [-2,1]

expected: "stable"

case 2

in: [2,1]

expected: "unstable"

case 3

in: [0,4]

expected: "center"

case 4

in: [0,-1]

expected: "saddle"

case 5

in: [3,0]

expected: "degenerate"

Starter codePython

def phase_stability(trace, det):
    # Your code here
    pass

5 test cases · run your code against them in the editor