Hi guys, suppose we have the following system of differential equations
X' = -aX + cY
Y' = aX - (b+c)Y + dZ
Z' = bY - dZ
where a,b,c,d > 0 and constant.
We can show that the system has non-zero constant solutions and that these satisfy
X/Y = c/a , Y/Z = d/b.
(This is easy to show)
But what I now need to do is show that for any initial data, the solution will tend to one of these solutions as t approaches infinity.
I have tried to find the eigenvalues for the system(using MAPLE) but this gets messy fast.
If anyone could help it would be much appreciated, cheers.