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Remark: Case (1): Equation 2.1 is linear, that is, f ( x, u ( x ) ) = f ( x ) Open image in new window.

Remark The case (ii) of Theorem 1.2 includes Theorem 1.1.

It should be remarked that case (1) is focused on the synchronization process, and cases (2) and (3) are associated to data transmission.

Following exactly the same arguments as in the base case, Remark 1 (and ) and Remark 2 (T L ) still hold for the current time (t+1).

Remark In the case that p = 1, the situationdegrades to the case of classical Orlicz norm. 1.

We remark that, the case when and, systems of type (1.1) have been extensively studied in the literature under different sets of conditions on the nonlinearities.

Remark 2 The case p = 1 has been proved in [1], so we will consider the case 2 n 2 n + 1 < p < 1 in this paper.

By Remark 4.1, this case cannot occur.

Remark 4.1 The case m T = 1 is trivial.

Remark 1.1 The case p > 1 of Theorem B was proved by Popoviciu [8].

Thus, using the XC code suitable for UMP, see Remark 4, this case is excluded.