Tag: Time Series

Estimating Lyapunov Spectra of ODEs using Python
Python code is shown that estimates the Lyapunov spectra for the Rossler and Lorenz systems. This code is written in a way that makes it adaptable for other continuoustime systems.

Modelling Chaotic Systems using Support Vector Regression and Python
Support Vector Regression is a technique in machine learning that can be used to model chaotic data. A program is shown to work on Delayed Henon Map data.

Lyapunov spectra of inverted discrete dynamical systems
One can estimate the lyapunov spectrum of dynamical systems and their inverted counterparts using local Jacobian matrices and Wolf’s algorithm.

Generating Poincaré Sections and Return Maps
Using the iterative 4th order RungeKutta method as described here, we can create low dimensional slices of the system’s attractor known as Poincare Sections, Return maps, or Recurrence maps. We will use the Rossler attractor for this example, with a, b, and c set to 0.2, 0.2, and 5.7, respectively. Poincare sections are important for visualizing…

Generating time series for Ordinary Differential Equations
We can produce a time series from ordinary differential equations by solving the equations using the iterative 4th order RungeKutta method and plugging each of the solutions back into the equations.

Modelling Sensitivity using Neural Networks
Artificial neural networks can be applied to the delayed Henon map and shown to replicate the sensitivities of the map surprisingly well.

Inverted Delayed Henon Map
Inverting the delayed Henon map yields a repellor whose sensitivities can be explored.

Delayed Henon Map Sensitivities
Partial derivatives can be used to explore how sensitive the output of a function is to perturbations in each of the time lags.