Phase Plane Sketcher
Use this tool to sketch the phase plane of a first order system of linear differential equations with constant coefficients
Enter your coordinates and in the left panel, and your phase plane is sketched on the right automatically as eight green phase curves. Eigenvalues and eigenvectors are also automatically calculated, and displayed on the left.
The moving blue dots indicate the directionality of the solutions as time increases from -1 to 1. To observe the motion over a longer time frame, increase
Timeframe using the slider.Note 1: The green phase curves only are plotted for times from -10 to 10 due to a limitation in GeoGebra, and so some systems--such as the system associated with the Owl & Mouse Predator & Prey populations--may not display the phase curves adequately. In particular, the phase curves may be too short to see when the axes have large scales. To get around this, try increasing
Timeframe to observe the dots over a longer period of time even though the phase curves themselves are not visible.
Note 2: This applet does not currently handle the case of repeated eigenvalues such as described in this article. So (from Example 1 in the link) will not return a phase portrait. Check back later; I may attempt to code this into an update in the future. Practice Suggestions:
Try replicating Example 1 from this article on Phase Portraits,.
For a preview of complex eigenvalues, check out the 2 example systems in this article on complex eigenvalues. Periodic example: . Note that the eigenvalues are purely complex. Spiral example: .
Also, try replicating the Mouse/Owl result from earlier. Pay close attention to which model we chose to be and which model we chose to be ! Remember, we have to respect this decision! I'll let you figure out and . Take your time. Also, read Note 1 above for a tip on what to expect.
Note to External Readers:
This applet is part of a GeoGebra "Book" on Differential Equations. If you like this, you may enjoy the book. Check it out here:
https://www.geogebra.org/m/cxgtwkqa