Based on the early developed approach for a NSP an analytical description, together with the social management redefinition, a possibility of the generalized approach application to the managing process is analyzed. The approach was reformulated in general form to be applied to a quantum size particles. Auto correlation function values were calculated for each of the two approach predicted regimes for the 3-rd order NSP development. The mechanisms of the revealed regimes were analyzed and associated with the "military" (ordered) and "civilian" (diffusive, disordered) transformations. One possible variant for a delay time nonmonotonic dependence of the auto-correlation function was shown to exist for the 1-st regime of the NSP development. The three possible variants 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 having decreasing and increasing dependence parts on the finishing stage of the development. The third variant has monotonously decreasing time dependence of the auto-correlation function. The above conclusions from the obtained results were shown to be confirmed by the relevant data from the modern and historical management practice.