Lyapunov Exponent Lite

Problem

Estimate the largest Lyapunov exponent with a Rosenstein-style lite method. Embed the series with dim and delay, find each point's nearest neighbor among the first m - steps points (excluding itself), measure the divergence steps ahead, and average log(d1 / d0) divided by steps.

Return 0.0 when parameters are invalid or no usable pairs exist.

Hint

Positive exponents indicate sensitive dependence on initial conditions.

Test cases

case 1

in: [[1,4,9,16,25,36,49,64],1,2,2]

expected: 0.2578490070148772

case 2

in: [[1,3,2,5,4,8,7,10],1,2,2]

expected: 0.15763680111818276

case 3

in: [[0,1,2,4,8,16,32,64],1,2,3]

expected: 0.653980211456134

case 4

in: [[1,2,1,2,1,2,1,2],1,2,1]

expected: 0

Starter codePython

import math
def lyapunov_exponent_lite(series, delay, dim, steps):
    # Your code here
    pass

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