Thank you for the suggestion and the URL.

Hey Greg Hannsgen you can use Wolfram Mathematica,

He's an example: http://demonstrations.wolfram.com/PhasePortraitAndFieldDirectionsOfTwoDimensionalLinearSystems/

Tremendous link. Thank you for the suggestion.

We have received some great advice and information. What about ways of computing phase diagrams for nonlinear systems? Again, what programs have people used to show the nullclines, etc. in this case, and what do the results look like?

Hello Greg,

I would personally recommend XPPAUT. It is a great dynamical systems and bifurcation program with many uses included plotting nulclines and creating bifurcation diagrams. The program takes a bit of getting used to but thankfully the creator (Bard Ermentrout) published an instruction manual to accompany the program. The program is freely available on Bard's website: http://www.math.pitt.edu/~bard/xpp/xpp.html

Thank you very much. I will definitely take a look at the program.

I am currently trying a menu-driven, stand-alone differential and difference equations program called PHASER with many helpful functions and find it helpful.

The website for the program is: http://www.phaser.com

One useful function, for example, creates bifurcation diagrams. However, the number of parameters appears to be limited to to 52--the upper case and lower case letters in the alphabet. The program is referred to in the book Dynamics and Bifurcations by Hale and Kocak, which can be purchased used for a small sum. The program is old but does seem to run on Windows 10.

Have you tried pplane? There is a javascript version