Numerical simulation of weak solutions of nonlinear stochastic differential equations in neighborhoods of bifurcation points

Authors: Khapisov M.Kh.
Published in issue: #4(105)/2026
DOI:
Category: Mathematics | Chapter: Computational Mathematics
Keywords: weak numerical methods, Brusselator, kinetic scheme, bifurcation point, phase portrait, attractor
Published: 18.09.2026

The study examines the application of numerical methods for simulating weak solutions of stochastic differential equations. First- and second-order methods were implemented and applied to investigate the behavior of solutions to the equation describing the response of a stochastic Brusselator. The stability condition for the solution of the stochastic Brusselator equation was verified. An analysis of the solution was carried out for both the subcritical and supercritical regimes. The transition from the subcritical to the supercritical case was examined, and the changes in the phase portrait of the solution arising during this transition were theoretically justified.

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