# Help on predator-prey differential equation

• Apr 28th 2008, 07:19 AM
keepitdk
Help on predator-prey differential equation
On Komodo Island, we have three species: Komodo dragons, deer, and a variety of plants.

The dragons eat the deer, the deer eat the plants, and the plants compete among themselves for the resources they need to grow.

Set up a system of differential equations that we can use to model the Komodo dragon (K), deer (D), and plant (P) populations.

Explain each term in your model and the parameters that appear in it.
• Apr 29th 2008, 05:30 AM
CaptainBlack
Quote:

Originally Posted by keepitdk
On Komodo Island, we have three species: Komodo dragons, deer, and a variety of plants.

The dragons eat the deer, the deer eat the plants, and the plants compete among themselves for the resources they need to grow.

Set up a system of differential equations that we can use to model the Komodo dragon (K), deer (D), and plant (P) populations.

Explain each term in your model and the parameters that appear in it.

To give a sensible answer to this we will need to know more about the real question or what you have been doing in class.

The Komododragons who appear to have no predators could have a rate of change of population determined by a logistic model:

$K'=a(D) K\left(1-\frac{K}{K_c(D)}\right)$

where $a(D)$ is the population growth rate coefficient for small populations and $K_c(D)$ is the carrying capacity of the island when there is a static population of dear $D$.

Then the eqivalent equation for dear might be:

$D'=b(P)D\left(1-\frac{D}{D_c(P)}\right)-c(D)K$

where the extra term represents the predation rate due to the Komodo dragon population.

You will also get a similar equation for the Plant population.

RonL