squircle_ode

squircle_ode, a MATLAB code which sets up and solves a system of ordinary differential equations (ODE) for a pair of functions that generalize the sine and cosine, and whose phase portrait is a squircle, a sort of squared circle.

Licensing:

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

Languages:

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

Related Data and codes:

squircle_ode_test

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

Reference:

• John D Cook,
  A generalization of sine and cosine,
  https://www.johndcook.com/blog/2020/12/21/generalization-sine-cosine/
• David Shelupsky,
  A generalization of the trigonometric functions,
  The American Mathematical Monthly,
  Volume 66, Number 10, December 1959, pages 879-884.

Source Code:

• squircle_conserved.m, evaluates a quantity that should be conserved for the ODE.
• squircle_deriv.m, returns the right hand side of the ODE.
• squircle_parameters.m, returns parameters for the ODE.