The evolution of cryptoeconomic systems through the prism of mathematical modeling of the dynamics of network interactions

Abstract

This article is devoted to the study of the evolution of cryptoeconomic systems through the prism of mathematical modeling of the dynamics of network interactions. The introduction substantiates the relevance of studying cryptocurrencies and blockchain technologies as new financial mechanisms capable of radically changing the global economic landscape. Modern cryptoeconomic systems are characterized by a high degree of complexity due to a multitude of interrelated entities, which requires the use of the latest mathematical analysis methods to identify the internal patterns of their development. The methodology section describes the tools and approaches used: graph theory, stochastic modeling, and methods for the dynamics of complex networks. The mathematical model proposed in the article makes it possible to study changes in network structures over time, take into account the nonlinearity of self-organization processes, and model the influence of external and internal factors on the stability of the system. Numerical experiments using real data from the crypto markets were used to verify the model, which made it possible to evaluate the accuracy and predictive power of the developed approach. The results of the study demonstrate that the dynamics of cryptoeconomic systems is subject to both random and deterministic changes associated with phase transitions and self-organization processes. The analysis showed that the key parameters of the models – the coefficients of interactions between network elements and the scale of nonlinear fluctuations – significantly affect the development of the system. The discussion of the results indicates the possibility of using mathematical modeling to predict crisis phenomena in the cryptoeconomy and develop recommendations for the stabilization of digital financial platforms. The final section highlights the importance of integrating mathematical models into the practice of analyzing cryptoeconomic systems. The data obtained can become the basis for the development of new management strategies aimed at increasing the stability and security of digital financial instruments. Thus, the presented research not only expands theoretical knowledge about the dynamics of network interactions, but also provides practical value for specialists in the field of cryptocurrencies, finance and mathematical modeling, contributing to the improvement of methods for analyzing complex economic systems.