Mira's Model!!!
HI
I know nothing about this guy Mira, I am looking at your equations just like any other one.
Just look at it as a parametric function, It seems that k is the varialbe. If there is no defined range for K, then you can try assuming to be a positive integer, lets say k= 1,2,..., N, You assume you inputs for X(1), Y(1), a and b, and that is all. This is obvious but I am writing it just for illustration
x(2) = b*y(1) + F(x(1)); and F can be caculated in the same way. Just numerical repetition.
cheers
Sal