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Order
The order of a dynamcial system or difference equation is the difference between the largest and the smallest arguments k appearing in it.
Examples
 y(k+1) = a(k)y(k)+b(k) has order 1
 y(k3)3y(k4) = 0 has order 1
 y(k+3)+ay(k+1) = by(k1) + c has order 4
 y(k+3) = 2/y(k2) + (k1) has order 5