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.