Competing Species Model with Two Species
This Demonstration illustrates the competing species model with two species, foxes and hawks. Foxes and hawks both prey on rabbits, of which there is a limited supply. The fox population is and the hawk population is ; both depend on time .[more]
1. In the absence of hawks, the foxes would grow logistically; thus when , where is the growth rate and is the carrying capacity for the fox population.
2. In the absence of foxes, the hawks would grow logistically; thus when , where is the growth rate and is the carrying capacity for the hawk population.
3. When both foxes and hawks are present, a sufficiently large number in either population will cause a decrease in the growth of both populations. Thus the model for competing species requires additional parameters and that determine the effect of large populations:
This example comes from , Section 7.3, Competing Species.
 J. R. Brannan and W. E. Boyce, Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, New York: John Wiley and Sons, 2010.