Strogatz 6.4 - Generalized Rabbit vs Sheep system
- Author:
- Justin Dunmyre
Use the sliders in the GeoGebra applet below to adjust the parameters for the Rabbit vs. Sheep system:
x' = x(a-x-by)
y' = y(c-x-y)
Play around with the nullclines, and see if you can make any conjectures about the stability of the critical point C, based on the configuration of the nullclines. Based on your conjecture, think about the long term behavior of solutions to the system. After you've made your prediction, toggle on the numeric solution slider to see if you were right!
It's a rewarding bit of algebra to try to prove your conjecture!
(Applet may take a moment to load)
If the applet is too slow for your tastes feel free to click on the three dots in the upper right corner of the screen to download it. It runs very well in the desktop app! Creating an account is free.