How can you find the critical points of the a predator prey model and solve the linear comparisonsystem corresponding to each critical point?

Then sketch thetrajectories in the vicinity of each?

Printable View

- Apr 13th 2009, 12:47 PMardampredator prey model
How can you find the critical points of the a predator prey model and solve the linear comparisonsystem corresponding to each critical point?

Then sketch thetrajectories in the vicinity of each? - Apr 13th 2009, 12:50 PMicemanfan
Presumably, the predator-prey model has an equation that models a relationship. Without that, you can't do anything.

- Apr 13th 2009, 12:52 PMardam
yer can use

x' = 5x − xy, y' = −2y + 3xy. - Apr 13th 2009, 12:58 PMicemanfan
Given a function $\displaystyle f(x,y)$, the critical points occur at $\displaystyle \frac{df}{dx} = 0, \frac{df}{dy} = 0$. Using your notation, this is where x' = 0 and y' = 0. So you have to solve that system of equations to find the critical points.

- Apr 13th 2009, 01:05 PMardam
so you sub these in and them find out x and y to be

x=2/3 and y=5? - Apr 13th 2009, 01:26 PMicemanfan
- Apr 13th 2009, 01:40 PMardam
- Apr 13th 2009, 01:49 PMicemanfan
Yes, there is only one critical point, which is the one you found. I'm afraid I don't know what "solving the linear comparison" refers to. The tangent plane to the surface $\displaystyle z(x, y)$ at that point is going to be $\displaystyle z = c$ for some constant c, because the surface is flat at a critical point. I don't know what else to say about it.

- Apr 13th 2009, 01:53 PMardam
it means to determine a relationship

between x and y (or between u and v for translated critical points).

Determine the type and stability of each critical point, and sketch the

trajectories in the vicinity of each.

Which im not too sure about

Its probably obvious