Pattern formation and diffusion-driven instability of a modified Lengyel-Epstein model

Authors

• Müge Meyvacı, Mimar Sinan Fine Art University, Department of Mathematics, Istanbul 34380, TürkiyeFollow
• Hüseyin Merdan, TOBB University of Economics and Technology, Department of Mathematics, Ankara 06530, TürkiyeFollow
• Yafia Radouane, Ibn Tofail University, Faculty of Sciences, Department of Mathematics, PB. 133, Kénitra, MoroccoFollow

Abstract

We consider a modified Lengyel-Epstein model that is covered by a system of reaction-diffusion equations and investigate the sufficient conditions on parameters of the model at which the diffusion-driven instability occurs. We perform numerical simulations to support and extend the theoretical findings. Analytical results and numerical simulations show that the modified Lengyel-Epstein system with positive initial and non-flux boundary conditions presents Turing patterns under some conditions on its parameters.

Recommended Citation

Meyvacı, Müge; Merdan, Hüseyin; and Radouane, Yafia (2026) "Pattern formation and diffusion-driven instability of a modified Lengyel-Epstein model," Mathematical Modelling and Numerical Simulation with Applications: Vol. 6: Iss. 3, Article 7.
DOI: https://doi.org/10.53391/2791-8564.1039
Available at: https://mmnsa.researchcommons.org/journal/vol6/iss3/7