Nonlinear ODEs in 2D
This application interactively plots the trajectories formed by two coupled first order ordinary differential equations. To obtain this program, first ensure that you already have Python 3 with Numpy, Matplotlib, Tkinter, and Sympy, and then download or clone this repository.
Usage
To open this program, run the file tkapp.py. This launches a GUI window showing a vector field plot of the differential equations with control widgets to the right.
To plot a trajectory starting from an initial condition, click anywhere on the vector field plot. To increase the speed at which this trajectory is rendered, move the Set simulation speed slider, which is found
near the bottom right of the GUI window. At the top of the GUI window are the two coupled first order differential equations, expressed as
x' = f(x, y) and y' = g(x, y). To change these equations, either select a preset from the Choose Preset Vector Field dropdown, or enter
a new equation using the Enter f(x, y) and Enter g(x, y) entry boxes. Any variable entered that is not x or y becomes parameters that you vary with the sliders.
To close this program, click the QUIT button.
References
Newman, M. (2013). Ordinary differential equations. In Computational Physics, chapter 8. CreateSpace Independent Publishing Platform.
Strogatz, S. (2015). Nonlinear Dynamics and Chaos. Boca Raton: CRC Press, https://doi.org/10.1201/9780429492563