This work is devoted to constructing a theoretical model of cryptocurrency micro-crises (sharp divergences in market participants’ expectations), in which regimes and their switching are intrinsic properties of the system rather than being externally imposed. The aim is to move from exogenous switching models to an endogenous model based on catastrophe theory. The main objectives are: (1) to formalize the model using stochastic polynomial relations; (2) to analyze the solutions of this system; (3)to derive the dynamic equations and develop a method for extracting roots.

The main results: a method for extracting stochastic roots is developed, resolving the problem of an infinite number of solutions; closed-form formulas are obtained for singular stochastic differential equations describing the dynamics of the stochastic roots of a polynomial; calibration of the model is presented using simulated data for the А+3 catastrophe, demonstrating the ability of the approach to reproduce key stylized facts of multimodality in time series. The obtained framework opens further prospects for risk management in highly volatile markets.