Lyapunov Exponent 1D Map

Problem

The Lyapunov exponent of the logistic map measures the average exponential separation of nearby orbits:

lambda = (1/n) * sum of ln|f'(x_k)| along the orbit.

Iterate x = r*x*(1-x) for n steps starting from x0, accumulating ln|r*(1 - 2x)| before each update, and return the average. A positive exponent signals chaos.

Hint

At r = 4 the theoretical Lyapunov exponent is ln(2), about 0.6931.

Test cases

case 1

in: [4,0.1,1000]

expected: 0.6934349555043721

case 2

in: [4,0.123456,500]

expected: 0.6939785071798493

case 3

in: [3.8,0.2,500]

expected: 0.41391435195894055

case 4

in: [4,0.3,2000]

expected: 0.6929468914389755

Starter codePython

def lyapunov_exponent(r, x0, n):
    # Your code here
    pass

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