Particle swarm optimization is often used to optimize functions in rather unfriendly non-convex, non-continuous spaces. The idea behind the algorithm involves a swarm of particles flying through a space both collaboratively and independently.
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 continuous-time systems.
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.
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One can estimate the lyapunov spectrum of dynamical systems and their inverted counterparts using local Jacobian matrices and Wolf’s algorithm.
Using the iterative 4-th order Runge-Kutta 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 [...]
