The software pplane allows the user to utilize a graphical interface to plot direction fields for differential equations. Instead of going through the hassle of defining array vectors of all points in the range of the desired differential equation graph, a user can simply enter their equations in the software, determine the desired range to graph, as well as the shape of the arrow.

This matlab package was written and developed by the professor of Rice University John C. Polking. He made this software free for use in educational institutions.

To run the software, download the following file pplane8.m. It has been tested to run on matlab R2019. After downloading the file, place it in a special folder, double click to open the .m file on matlab R2019, then press run.

pplane is a great program that makes it very easy to tackle nonlinear time-invariant differential equations of two states. Not only can you generate the field, but you can plot a phase portrait with trajectories of your choice and can then plot each of those state trajectories against time to see how the system actually evolves in finite time. It's a nice front-end to lots of other matlab utilities that makes it easy to get through your first course in nonlinear systems.

This picture shows the setup screen for using the pplane software. Set up the desired parameters for the differential equations on this screen.

Observe that this picture shows the direction field for the differential equation.

Observe that by changing the minimum and maximum value of x and y the range of the plotted direction field changes.

By clicking on an arrow on the direction field, the orbital of the differential equation will be shown.

 

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