In general terms, non-conservation is introduced ad-hoc into the equat
ions, in order to get a realistic description. Whether conservative or
not, the behavior of the solution is univocal. Here we study two coup
led difference logistic equations. Now the system is not univocally co
nservative: during a period of time, it will be conservative with Haur
sdorff dimension D-H less than or equal to 1 and finally, a smallest p
erturbation will get over dimension 1 less than or equal to D-H less t
han or equal to 2.