Thanks to both, actually I was too sketchy:
my system would look like this :
Apß=Bp,
with A and B square matrices, p vector and ß single variable. (A and B are like Leontiev input/output matrices)
Left term is at the beginning of first cycle, right one at the end.
The elements of A are given at the beginning, the ones in B are calculated from those in A (following some rules and conditions).
p is supposed to be a unique solution, together with ß, that satisfies all preconditions.
On second cycle A changes (using the values of B..), so will as a consequence p ( ß too should). And so on..
So we don't have explicit dependance on a continuos time, but a sequence of matrices (A(t) , with t discrete).
I couldn't find out how to write this process.