As a result of the application of recurrence quantification analysis to acoustic emission time series obtained in uniaxial tensile testing of copper and silver, we detected the existence of a characteristic interval in which the Shannon information entropy (as a parameter of the quantitative analysis of recurrence plots) increased rapidly. Using statistical analysis of the behavior of the dislocation ensemble, we established a relation between the physical parameters of the given interval and the global stability loss parameters of the plastic flow of metals, indicating the predictability of the distinctive point determined long before the critical state was attained.