SUSTAINABILITY ANALYSIS OF AN ADAPTIVE DIGITAL ENTERPRISE BUSINESS MODEL IN A MULTI-COMPONENT SYSTEMS

This paper develops a mathematical model of an adaptive business model for a digital enterprise operating in a multi-component environment and proves the conditions for its sustainability. The relevance of the research is determined by the fact that modern organizations are simultaneously exposed to physical, institutional, market, and technological factors; however, existing approaches consider these factors in isolation and do not provide formal justification for viability conditions. The methodological framework of the study integrates active systems theory, system dynamics, and nonlinear control theory. A causal loop diagram and a stock-flow diagram were constructed using the VENSIM simulation environment. The Input-to-State Stability (ISS) concept and the Lyapunov function method were applied for formal stability analysis. As a result, a model with two feedback loops was developed — a stability loop and an adaptation loop, with switching between them occurring through a critical stress threshold. The system was proven to possess ISS stability under three simultaneous conditions: boundedness of the external perturbation flow function, positive sensitivity of adaptation capacity to buffer magnitude, and positivity of the buffer replenishment function during stability periods. Numerical simulation of three scenarios confirmed the theoretical predictions and demonstrated the existence of an equilibrium attraction domain. The results expand the possibilities for quantitative analysis of organizational sustainability and can be applied for early threat detection, investment decision support, and digital platform strategy development.