One of the most striking features for deterministic chaotic systems is the limited predictability (or unpredictability) of the future evolution of the system, despite the determinism of the system.
The Lyapunov exponents are related to the average rates of divergence and /or convergence of nearby trajectories in phase space, and therefore, the measure how predictable or unpredictable the dynamical system is. In other words, they express the loss of information in time and are usually express in units of an inverse of time.
from math import log import numpy as np with open('data.txt', 'r') as f: data = [float(i) for i in f.read().split()] N = len(data) eps = 0.001 lyapunovs = [[] for i in range(N)] for i in range(N): for j in range(i + 1, N): if np.abs(data[i] - data[j]) < eps: for k in range(min(N - i, N - j)): lyapunovs[k].append(log(np.abs(data[i+k] - data[j+k]))) with open('lyapunov.txt', 'w') as f: for i in range(len(lyapunovs)): if len(lyapunovs[i]): string = str((i, sum(lyapunovs[i]) / len(lyapunovs[i]))) f.write(string + '\n')
You can get more information here, such as the structure of your data file:
https://blog.abhranil.net/2014/07/22/calculating-the-lyapunov-exponent-of-a-time-series-with-python-code/
Hi!
The nolds Python package might help you:
https://pypi.org/project/nolds/
This link seems promising as well:
http://systems-sciences.uni-graz.at/etextbook/sw2/lyapunov.html
Best regards, Gerrit
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