langford_ode

langford_ode, a Python code which sets up and solves the Langford ordinary differential equation (ODE) which has chaotic behavior and an attractor.

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license.

Languages:

langford_ode is available in a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

python_ode, a Python code which sets up various systems of ordinary differential equations (ODE).

Reference:

1. William Langford,
   Numerical studies of torus bifurcations,
   Internationale Schriftenreihe zur numerischen Mathematik,
   Volume 70, Birkhaeuser, 1984, pages 285-295.
2. Stephen Lucas, Evelyn Sander, Laura Taalman,
   Modeling dynamical systems for 3D printing,
   Notices of the American Mathematical Society,
   Volume 67, Number 11, December 2020, pages 1692-1705.

Source Code:

• langford_ode.py, the source code.
• langford_ode.sh, runs all the tests
• langford_ode.txt, the output file.

• langford_ode_components.png, a plot of (T,X(T)), (T,Y(T)), and (T,Z(T)).
• langford_ode_3d.png, a 3D plot of (X(T),Y(T),Z(T)).