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


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


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).


  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:

Last revised on 07 March 2024.