The paper is devoted to studying the stability of complex systems, which include diversified and heterogeneous elements. In order to analyze the stability of such systems, it is proposed to develop the process of dynamic determination of the main factors. For this purpose, this paper uses a variant of cognitive modeling based on the concept of “influence”. The proposed approach implies, in a sense, a broader view of the concept of the “fuzzy cognitive map” introduced by B. Kosko. “Influence” does not mean “causality”, allows a broader interpretation range, and is calculated in a special way that makes it possible to prove rigorous theorems. A complex system is represented as a digraph, and the selection of the main factors is proposed to be based on the concept of “influence”, which is introduced as follows. All nodes of the graph are assigned an abstract property “significance”, which allows you to compare heterogeneous factors, and a particular computational procedure is introduced that allows this “significance” to be calculated. The “influence” of factors on each other is defined as a mathematically formalized response in accordance with the introduced computational procedure of the “significance” of the studied factor to the variation in the “significance” of input factors. For example, the analysis of the sustainability of a large-scale model of the Russian economy in terms of the strength of the “influence” is provided.