How can I correctly specify and solve a system of delay difference equations in mathematica similar to NDSolve with regard to delay differential equations?
For example if I want to "see" the values explicitly with RecurrenceTable and my system of equations has the following form:
a[n+1] =b[n]+c[n-1], b[n+1]= a[n-1]+c[n], c[n+1]= b[n-1]-a[n]
I am not sure how to specify the initial conditions like it is done with a initial history function with delay differential equations like the following system for example:
NDSolve[{a'[t] == -a[t] + c[t - 1], b'[t] == -b[t] + a[t-1],
c'[t] == -c[t] + b[t - 1], a[t /; t <= 0] == 1, b[t /; t <= 0] == 2,
c[t /; t <= 0] == 3}, {a, b, c}, {t, 0, 20}]
I hope it is clear what I mean and hope for some helpful hints :)