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The article discusses the theoretical and methodological foundations of the analysis of the dynamic stability of socio-economic systems in the context of nonlinear transformations and increasing uncertainty of the external environment. The necessity of transition from a static equilibrium paradigm to a dynamic representation of stability as a characteristic of the trajectory of the system development is substantiated. Based on the synthesis of the theory of dynamic systems and economics, an integrated conceptual and mathematical basis for the study of dynamic stability has been formed. A classification of linear, nonlinear, stochastic, and entropic stability models is proposed, and their analytical capabilities and limitations are identified. A generalized dynamic model has been developed that takes into account nonlinearity, lag effects, and feedbacks. A system of criteria for assessing dynamic stability is formulated, including Lyapunov, structural, stochastic and institutional components. An algorithm for assessing the dynamic stability of socio-economic systems is presented and the role of adaptive capacity and "soft" management in preventing critical transitions is shown.
dynamic stability, nonlinear dynamics, stochastic models, entropy approach, adaptive potential, feedback, phase trajectories, dynamic programming
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