Method for Analyzing Economic Processes in Conditions of Instability (on the Example of Analyzing the Dynamics of Revenue of Russian Companies)

New methods are proposed that allow using the properties of nonlinear dynamics models to analyze the dynamics of real socio-economic processes. For this, a complex of models has been developed in the form of connected nonlinear one-dimensional and multidimensional map pings that meet the general laws of socio-economic processes – development in a rapidly changing environment under resource constraints. The proposed set of models allows you to analyze the dynamics of processes under the assumptions of both their independence and interconnection with each other. The definition of interrelated processes is introduced as processes developing under conditions of general constraints. Three criteria are proposed for identifying interrelated processes based on empirical data. In the case of interrelation of processes, the parameters of one-dimensional and multidimensional models are also interrelated, which allows a deeper analysis of the situations under consideration. The use of the proposed method is demonstrated by the example of analyzing the dynamics of revenue of Russian companies in the pe­riod from 2006 to 2015 (38 thousand companies in total). All companies were divided into four groups, depending on the rate of revenue growth from 2010 to 2015. The hypothesis of a possible relationship between the decline of one and the parallel strengthening of another group of Russian firms after the crisis of 2008–2009 is investigated and rejected. Innovative firms that boosted their revenue growth potential after the crisis were targeting markets other than con ser­vative firms whose revenue growth potential was exhausted after the crisis. The peculiarities of the dynamics of revenue of groups of companies are visually presented in the form of normalized values, when the median estimates of each of the groups in 2007 are taken as a unit.