Based on the early developed analytical approach for 3-rd order non-stationary stochastic processes (NSP-s) development a possibility of the generalized approach application to the managing process is analyzed. The approach was reformulated in general form to be universally applied to a quantum size particles, assumedsimultaneously participate in the following type of motion: 1) chaotic oscillation in nano-scale, 2) translation theirselfs in macro-scale. In the 1-st part of the article autocorrelation function (ACF) values were calculated for each of the two predicted by the approach regimes for NSP-s development. Only one possible variant for a delay time nonmonotonous dependence of the ACF was shown to exist for the 1-st regime of the non-stationary stochastic processes development. The mechanisms of the revealed two regimes were analyzed and associated with the "military" (ordered) and "civilian"(diffusive, disordered) energy transferring. The three possible variants for the delay time dependencies were observed for the 2-nd regime. Two of the variants were analogous each other in conserving similar, relatively high ordering levels for the most time periods of their developments but havingdecreasing and increasing the dependence parts on the finishing stage of the regime development. The third variant has monotonously decreasing time dependence of the ACF. In the 2-nd part of the article, conditions for development the revealed two regimes of a NSP development were analyzed in detail. Based on the widely used principle of "analogy"for NSP-s in the Universe it was shown that the revealed NSP regimes have to develop practically simultaneously to provide the policystals highplasticity. The analogous conclusion is supposed to be truth for a NSP management. The obtained conclusions were shown to be confirmed by the relevant data from the modern and historical management practice.