Lois Lyman, who wrote "Wiscasset Schooners" and the "Going On" song (both recorded by Gordon Bok, among others) has an "Alpha Cat" song:

Oh I'm an alpha kitty, I am a alpha cat.

I'm fluffy and tough and I got the right stuff

'Cause I'm the alpha cat.

Unfortunately I do not believe it has yet been recorded.

Dan