🚀 go-pugleaf

Given a system of nonlinear difference equations,

	x(k+1) = F ( x(k), y(k-1) )
	y(k+1) = G ( x(k-1), y(k) )

I would like to perform some kind of linear stability
analysis around the point (x*, y*).
I believe that the only way to do so is by augmenting
the system, while introducing two more variables
z(k) and w(k) so that the augmented systems looks like :

	x(k+1) = F ( x(k), z(k) )
	y(k+1) = G ( w(k), y(k) )
	z(k+1) = y(k) 
	w(k+1) = x(k) 

Now I can linearize and study the stability behavior of 
the linearized systems around (x*, y*). In other words
before I proceed to the linearization I must have my 
indices such that my equations read :
	
	L.H.S. (k+1) = R.H.S (k).

Any comments on such an approach ? Any references would
be appreciated.
Thank you,
ioannis

androula@ecn.purdue.edu
	
p.s. Similar arguments hold for larger delayed arguments
as well.