Algodoo

Edit:
- slight changes to the code to increase performance. This allows the "law of big numbers" to take effect. The resulting graphs are much closer to the differential equations and much more consistent over time. You can play the simulation at up to 4x sim speed to get results faster.

Content
This simulation aims to recreate the dynamic equilibrium of the "Lotka-Volterra-equations". Those represent the influence the population of a hunter animal has on the reproduction rate of its prey animal and vice versa.
Here the hunters are represented as red circles (as soon as the sim starts) and their prey are yellow dots. When colliding yellow dots will turn into red circles, representing the idea, that the hunter successfully fed itself and its offspring. Failing to eat will result in death for the hunters. Prey dots will eventually reproduce unless eaten. The green patches are safe zones for prey animals which cannot be entered by hunters.
Currently the dynamic equillibrium will be maintained for about 3-10 minutes. Eventually either all prey gets eaten and the hunters die out shortly after, or (more likely) the hunters die out and prey will reproduce exponantially and indefinitely.

You can change the odds of those events and the time of their occourence by...
... changing the location, size and amount of Objects (green bushes/trees)
... changing the location, size and amount of safe zones (green patches)
... changing the time it takes to starve to death for hunters or reproducing for prey
--> right-click on one of the black dots before starting --> script menu --> onSpawn: change the variables or their randomness factor then save and restart the simulation for it to be applied.

Have fun and let me know if you can optimize the variables for a higher duration and better results!