Competing Species Model with Two Species

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram CDF Player or other Wolfram Language products.

Requires a Wolfram Notebook System

Edit on desktop, mobile and cloud with any Wolfram Language product.

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:

,

.

[less]

Contributed by: Laura R Lynch (May 2015)
Open content licensed under CC BY-NC-SA


Snapshots


Details

This example comes from [1], Section 7.3, Competing Species.

Reference

[1] 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.



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send