Question

equilibrium solutions to system of equations
dr/dt=2*R*(1- R/2) - 1.2*R*F
dF/dt=-F + 0.9*R*F

Answer 1

???

the system is in equilibrium when, dF/dr = 0

Answer 2

yes it is

Answer 3

dF/dr = dF/dt * dt/dr = (-F + 0.9*R*F)/(2*R*(1- R/2) - 1.2*R*F) = 0

Answer 4

this is where I'm not sure how to do this. I have three points but I dont know if that is all

Answer 5

(-F + 0.9*R*F) = 0
R = 1/0.9

Answer 6

yes I have (0,0), (2,0), and (10/9,20/27)

Answer 7

I am just doing this by intuition, is there some more systematic way of doing it?

Answer 8

dF/dR = (-F + 0.9*R*F)/(2*R*(1- R/2) - 1.2*R*F)
equate it to zero , (-F + 0.9*R*F)/(2*R*(1- R/2) - 1.2*R*F) = 0
and solve for R, answer is, R = 10/9

To find F, integrate or solve this differential equation
dF/dr = (-F + 0.9*R*F)/(2*R*(1- R/2) - 1.2*R*F)
F = F(R), put the value of R=10/9
you should get 20/27

Answer 9

so is there only 3 equilibrium points?

Answer 10

because (0,0) and (2,0) are solutions alos

Answer 11

not sure ... but this must be sure for one, r = 10/9

Answer 12

hmm yeah I need all, and many times there are more than one. (0,0) and (2,0) you can see from looking at it but some are more dificult to get to.

Answer 13

wolf's gone crazy
http://www.wolframalpha.com/input/?i=dF%2FdR+%3D+%28-F+%2B+0.9*R*F%29%2F%282*R*%281-+R%2F2%29+-+1.2*R*F%29

Answer 14

yeah haha tnx m8