@article{Yang2025, 
author = {Jia Yu Yang and Yu Lan Wang and Zhi Yuan Li},
title = {Exploring dynamics and pattern formation of a fractional-order three-variable Oregonator model},
year = {2025},
journal = {Networks and Heterogeneous Media},
volume = {20},
number = {4},
pages = {1201-1229},
keywords = {fractional Oregonator model, Grünwald–Letnikov derivative, turing instability, spatiotemporal patterns, weakly nonlinear analysis},
url = {https://www.sciopen.com/article/10.3934/nhm.2025052},
doi = {10.3934/nhm.2025052},
abstract = {In this paper, we investigated the nonlinear dynamics and pattern formation of a fractional-order three-variable Oregonator model. We first performed a linear stability analysis of the model without diffusion, deriving equilibrium points and Jacobian eigenvalues, and verified Matignon's stability conditions. A high-precision numerical scheme was developed, and simulations revealed that even tiny variations in fractional order produce significant changes in long-term trajectories. For the reaction-diffusion model, we analyzed Turing instability under integer-order diffusion and derived the critical wave-number conditions via Routh-Hurwitz criteria. Weakly nonlinear analysis near the Turing threshold yielded coupled amplitude equations whose coefficients predicted stripe, hexagon, and mixed patterns. Extensive two-dimensional numerical experiments confirmed the theoretical predictions: Depending on diffusion coefficients and other parameters, the model evolved into bullseye, spiral, labyrinthine, or spot-stripe mixtures.}
}