Walsh Function Approximation Applied to Two-Dimensional Stochastic Brusselator Model

A numerical study published in Discover Applied Sciences presents a computational investigation of the stochastic Brusselator model, a two-dimensional nonlinear chemical reaction system subject to random fluctuations. The researchers developed a computational approach based on Walsh function approximation to simulate how internal noise affects the system’s oscillatory chemical dynamics.

In the governing formulation of the two-dimensional model, stochastic perturbations are incorporated through Wiener processes. These Wiener processes are utilized to simulate the specific impact of internal noise on oscillatory chemical dynamics within the nonlinear reaction system.

To carry out the numerical computation, the authors used Walsh function approximation to reduce the nonlinear stochastic integral equation to a system of algebraic equations. The resulting algebraic system was then solved numerically using a systematic algorithm tailored specifically to the two-dimensional Brusselator model.

Numerical experiments reported in the study demonstrate the efficiency and accuracy of the suggested computational method. In addition, the researchers presented graphical solutions across various parameter values to illustrate the influence of noise on the behavior of the two-dimensional system.

Subject of Research: Numerical computation of the two-dimensional stochastic Brusselator model

Article Title: Walsh function approximation for numerical computation of the 2-dimensional stochastic Brusselator model

Article References: Mallik, L., Paikaray, P. P., Parida, N. C., Beuria, S., & Izadi, M. (2026). Walsh function approximation for numerical computation of the 2-dimensional stochastic Brusselator model. Discover Applied Sciences. https://doi.org/10.1007/s42452-026-09827-z

Image Credits: AI Generated

DOI: 10.1007/s42452-026-09827-z

Keywords: stochastic Brusselator model, Walsh function approximation, numerical computation, chemical reaction dynamics, Wiener processes, stochastic perturbations, nonlinear integral equations, internal noise, Walsh, function, approximation, numerical