Premium
On the stability and nonexistence of turing patterns for the generalized Lengyel‐Epstein model
Author(s) -
Abdelmalek S.,
Bendoukha S.,
Rebiai B.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4457
Subject(s) - mathematics , stability (learning theory) , turing , mathematical economics , mathematical analysis , pure mathematics , computer science , programming language , machine learning
This paper studies the dynamics of the generalized Lengyel‐Epstein reaction‐diffusion model proposed in a recent study by Abdelmalek and Bendoukha. Two main results are shown in this paper. The first of which is sufficient conditions that guarantee the nonexistence of Turing patterns, ie, nonconstant solutions. Second, more relaxed conditions are derived for the stability of the system's unique steady‐state solution.