Understanding Predator-Prey Systems with HPGSystemSolver

[APool555]

I tried reading some of the examples in my textbook(Differental Equations by Paul Blanchard), and I ended up confusing myself more than anything else. Here's the problem:

dR/dt= 2R(1-R/2.5)-1.5RF
dF/dt= -F+0.8RF

Sketch the R(t) and F(t) graphs for the solutions with initial points A,B,C, and D.(these points are on a graph I have)
How can I find the values of these points and how do I get the equation to graph the R(t) and F(t) graphs?

Thanks.

 

[Tide]

Short of fully solving the system of equations I think the operative word is "sketch." You have some information (which you haven't provided here) regarding the "initial points." What kind of a graph is it? Does it have numbers?

You can get some idea of the behavior of the graphs by tracking the slopes of the curves for various intitial conditions. For example, if the rabbit population were about 2.5 then clearly you would see the rabbit population decreasing. Depending on the relative size of the fox population, in this case, you would see the fox population either increasing or decreasing. If the fox population falls too much you'll see the rabbit population go up. It's somewhat qualititative but you can't do much more unless you solve the system.

 

[Yann]

You should use the "HPGSystemSolver.exe" on the CD with the book, with it you can plot the system and try it with different initial conditions.