An approach to the identification of non-linear maximally stationary systems is proposed, based on the use of a
consistent measure of dependence of the input and output processes of the system under study. In accordance with the
conventional terminology, a measure of dependence between two random values (processes) is referred to as
consistent, if it vanishes if and only if the values (processes) are stochastically independent. Within the consideration
subject, such a measure of dependence is the maximal correlation. In turn, the maximally stationary systems are those,
for which the first eigenfunctions, corresponding to the largest in the absolute value first eigenvalue of the joint
probability distribution density expansion, do not depend on the time.