attractor_ode

attractor_ode, a MATLAB code which sets up and solves several systems of ordinary differential equations (ODE) which have chaotic behavior and an attractor, with the Lorenz ODE being a classic example.

Licensing:

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

Languages:

attractor_ode is available in a MATLAB version.

Related Data and codes:

attractor_ode_test

matlab_ode, MATLAB codes which set up various ordinary differential equations (ODE).

Reference:

1. Vadim Anishchenko, Vladimir Astakhov,
   Experimental study of the mechanism of the appearance and the structure of a strange attractor in an oscillator with inertial nonlinearity,
   Radiotekhnika i Elektronika,
   Volume 28, 1983, pages 1109-1115.
2. Alain Arneodo, Pierre Coullet, Edward Spiegel, Charles Tresser,
   Asymptotic Chaos,
   Physica D: Nonlinear Phenomena,
   Volume 14, Number 3, 1985, pages 327-347.
3. Guanrong Chen, Tetsushi Ueta,
   Yet another chaotic attractor,
   International Journal of Bifurcation and Chaos in Applied Sciences and Engineering,
   Volume 9, Number 7, 1999, pages 1465-1466.
4. Peter Gray, Stephen Scott,
   Chemical oscillations and instabilities,
   Interational Series of Monographs on Chemistry,
   Volume 21, Oxford University Press, 1990.
5. Michel Henon, Carl Heiles,
   The applicability of the third integral of motion: some numerical experiments,
   Astronomical Journal,
   Volume 69, 1964, pages 73-79.
6. William Langford,
   Numerical studies of torus bifurcations,
   Internationale Schriftenreihe zur numerischen Mathematik,
   Volume 70, Birkhaeuser, 1984, pages 285-295.
7. Edward Lorenz,
   Deterministic Nonperiodic Flow,
   Journal of the Atmospheric Sciences,
   Volume 20, Number 2, 1963, pages 130-141.
8. 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.
9. Michael Mackey, Leon Glass,
   Oscillation and chaos in physiological control systems,
   Science,
   Volume 197, Number 4300, pages 287-289, 1977.
10. Otto Roessler,
    An equation for continuous chaos,
    Physics Letters,
    Volume 57A, Number 5, pages 397–398, 1976.

Source Code:

• anishchenko_deriv.m, the right hand side of the Anishchenko ODE.
• anishchenko_parameters.m, parameters of the Anishchenko ODE.
• arneodo_deriv.m, the right hand side of the Arneodo ODE.
• arneodo_parameters.m, parameters of the Arneodo ODE.
• autocatalytic_deriv.m, the right hand side of the autocatalytic ODE.
• autocatalytic_parameters.m, parameters of the autocatalytic ODE.
• chen_deriv.m, the right hand side of the Chen ODE.
• chen_parameters.m, parameters of the Chen ODE.
• henon_heiles_deriv.m, the right hand side of the Henon Heiles ODE.
• henon_heiles_parameters.m, parameters of the Henon Heiles ODE.
• langford_deriv.m, the right hand side of the Langford ODE.
• langford_parameters.m, parameters of the Langford ODE.
• lorenz_deriv.m, the right hand side of the Lorenz ODE.
• lorenz_parameters.m, parameters of the Lorenz ODE.
• roessler_deriv.m, the right hand side of the Roessler ODE.
• roessler_parameters.m, parameters of the Roessler ODE.