• ## 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.

• ## Automatically Link Text using VB.Net

Automatically add HTML to link any words with http:// or https:// within text using this VB.net script

• ## Generating Poincaré Sections and Return Maps

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 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 4-th order Runge-Kutta method and plugging each of the solutions back into the equations.

• ## GET/POST to a URL in Python

A relatively simple and straightforward way to post information to a server using Python

• ## 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.

• ## Subgraph Centrality

Subgraph Centrality: Accounts for the participation of a node in all subgraphs of the network

• ## Freeman’s Approach to Degree Centrality

Freeman’s Approach to Degree Centrality: Centrality is based on connections between nodes in the network