Bifurcations and pattern formation in a generalized Lengyel-Epstein reaction-diffusion model

被引：8
作者：
Mansouri, Djamel [1 ,2 ]
Abdelmalek, Salem [2 ,3 ]
Bendoukha, Samir [4 ]
机构：
[1] Univ Abbes Laghrour, Dept Math, Khenchela, Algeria
[2] Larbi Tebessi Univ, Lab Math Informat & Syst LAMIS, Tebessa, Algeria
[3] Larbi Tebessi Univ, Dept Math & Comp Sci, Tebessa, Algeria
[4] Taibah Univ, Elect Engn Dept, Coll Engn Yanbu, Medina, Saudi Arabia
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 132卷
关键词：
General lengyel-Epstein model; Reaction-diffusion; Hopf-bifurcation; Pattern formation; TURING PATTERNS; SYSTEMATIC DESIGN; OSCILLATIONS; STABILITY;
D O I：
10.1016/j.chaos.2019.109579
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper investigates the formation of spatial patterns in a general reaction-diffusion system based on the Lengyel-Epstein CIMA model. By analyzing the properties of the system's unique positive equilibrium in the ODE and PDE cases, we establish the existence of non-constant steady state solutions thereby confirming the existence of Turing instability. Hopf-bifurcation analysis of the system show the existence of periodic solutions in the absence and presence of diffusion. Numerical simulations are presented to validate the theoretical results of the paper. (C) 2019 Elsevier Ltd. All rights reserved.
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页数：9
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