Linearisation of coupled map

[matthewv525]

I have a 2D system

x_n+1 = f(x_n) + y_n - y_n-1yn+1 = g(y_n) + x_n - x<sub>n-1

and I want to linearise it about the fixed points (x*,y*)</sub>

letting
&x_n = x_n- x*
&y_n = y_n- y*

would this be correct?

&x_n+1 = f'(x*)&x_n + &y_n - &y_n-1

&y_n+1 = g'(y*)&y_​n + &x_n - &x<sub>n-1

thanks in advance</sub>