MediumCalculusca-172

Bifurcation Parameter Check

Problem

The logistic map has the nonzero fixed point x* = 1 - 1/r for r > 1, with multiplier f'(x*) = 2 - r.

The fixed point is attracting when |2 - r| < 1, that is for 1 < r < 3. Given r, return True when the fixed point is stable and False otherwise.

Hint

At r = 3 the multiplier reaches -1 and the period-doubling cascade begins.

case 1

in: [2.5]

expected: true

case 2

in: [3.2]

expected: false

case 3

in: [3]

expected: false

case 4

in: [1.5]

expected: true

case 5

in: [0.5]

expected: false

Starter codePython

def bifurcation_stable(r):
    # Your code here
    pass

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