MATHEMATICAL ANALYSIS OF MARKET EQUILIBRIUM STABILITY

This article presents a systematic review of mathematical methods for analyzing market equilibrium stability under contemporary economic instability. The study examines classical market adjustment concepts of Walras and Marshall, mathematical apparatus of dynamical systems theory including linearization method and Lyapunov direct method, as well as modern extensions of basic models to cases of imperfect information, time delays, and stochastic perturbations. A comparative analysis of stability under different market structures from perfect competition to oligopoly is conducted. Practical recommendations for selecting analytical methods depending on market characteristics are formulated. Promising directions for future research are identified, including development of constructive methods for building Lyapunov functions for high-dimensional systems and creation of early warning systems for crises based on stability loss indicators.