2023/08/23 by Aldo Ledesma–Durán, Ledesma-Durán, Aldo
Computer Science · #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.2308.12360
openalex publication_date 2023/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We propose conditions for the emergence of Turing patterns in a domain that changes in size by homogeneous growth/shrinkage. These conditions to determine the bifurcation are based on considering the geometric change of a potential function whose evolution determines the stability of the trajectories of all the Fourier modes of the perturbation. For this part of the work we consider the situation where the homogeneous state of the system are constant concentrations close to its stationary value, as occurs for exponential growth/decrease. This proposal recovers the traditional Turing conditions for two-component systems in a fixed domain and is corroborated against numerical simulations of increasing/decreasing domains of the Brusselator reaction system. The simulations carried out allowed us to understand some characteristics of the pattern related to the evolution of its amplitude and wavenumber and allow us to anticipate which features strictly depend on its temporal evolution.