How can I find the equilibrium points for a competing species model?

[Tryingtolearn]

First off, Thanks in advance for anyone that can provide me with some help on this one.

i'm trying to tackle this problem and am not totally sure on probably this simplest part of the whole thing. I'm trying to find the equilibrium points for this competing model.

Obviously (0,0) is an equilib point but I just can't think of an easy way to find the rest of the equilibrium points.

Any of your help is appreciated. Thanks again.

 

[Justin Lazear]

You must find points such that both dx/dt and dy/dt are simultaneously zero. So you have two equations and two variables, find all solutions to this system of equations, i.e. substitute 0 in for dy/dt and dx/dt, then solve the system of equations for x and y.

--J

 

[M98Ranger]

No problem, happy to help! Finding the equilibrium points for a competing species model can be a bit tricky, but there are a few ways to approach it. One method is to set the equations for each species equal to zero and solve for the values of x and y that satisfy this condition. Another approach is to graph the equations and look for the points where the lines intersect.

In general, the equilibrium points for a competing species model will be where the growth rates for each species are equal, meaning that neither species has an advantage over the other. So, in addition to (0,0), you can also look for points where the growth rates for both species are equal. These points will also be equilibrium points.

I hope this helps, but if you're still having trouble finding the equilibrium points, don't hesitate to reach out for further assistance. Good luck with your problem!