Fox and Rabbit Population Stability Analysis

Authors: Alex Tee Neng Heng, David G. Green

The foxes and rabbits model is a predator-prey dymnamic system. A dynamic system is a set of interrelated variables whose values change through time. Each population has 3 variables:

  • Initial population
  • Birth rate (0 – 1)
  • Death rate (0 – 1)

This model assume that the populations of fox, F_i and rabbit, R_i at time i are related by the formula below:



  • Increase the initial size of the fox population by 1. What happens to the two curves? Based on this result is the equilibrium stable?
  • Try altering the values for the birth and death rate. Can you find a set of values for which a limit cycle occurs?

Demo screenshot