The article proposes a state-dynamic approach to the analysis of phase transitions in complex CRM systems (customer relationship management systems), aimed at modeling and predicting mass customer behavior. Based on the analogy between socio-economic processes in interaction with customers and physical phase transitions, a mathematical model is proposed that takes into account critical points of change in behavioral states. Numerical modeling using the Monte Carlo method is used to analyze critical phenomena and determine stability conditions. Phase diagrams are obtained that demonstrate the change in customer segments in response to changes in key marketing parameters. A comparative analysis with existing CRM models is conducted and empirical testing is carried out on real data from commercial companies. The results obtained allow a deeper understanding of the mechanisms of collective customer behavior and to propose effective strategies for managing CRM systems.
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