MULTIPLE-PEAK TRAVELING WAVES OF THE GRAY-SCOTT MODEL

被引：0

作者：

Chen, Xinfu ^{[1
]}

Lai, Xin ^{[2
]}

Qi, Yuanwei ^{[3
]}

Qi, Cong ^{[4
]}

Zhang, Yajing ^{[5
]}

机构：

[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

[2] Civil Aviat Univ China, Coll Sci, Tianjin 300300, Peoples R China

[3] Univ Cent Florida, Dept Math, Orlando, FL 32816 USA

[4] Natl Univ Singapore, Ctr Quantitat Finance, 6 Sci Dr 2, Singapore, Singapore

[5] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

MATHEMATICS IN APPLIED SCIENCES AND ENGINEERING | 2023年 / 4卷 / 03期

基金：

美国国家科学基金会;

关键词：

Gray-Scott model; Multi-peak traveling wave; Singular perturbation; Complex Pattern; REACTION-DIFFUSION SYSTEMS; CHEMICAL-REACTION MODEL; SPIKE AUTOSOLITONS; SELF-SIMILARITY; STEADY-STATES; STABILITY; DYNAMICS; PATTERNS; EXISTENCE; REACTOR;

D O I：

10.5206/mase/16513

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a reaction-diffusion system which models the pre-mixed isothermal autocatalytic chemical reaction of order m (m > 1) between two chemical species, a reactant A and an auto-catalyst B, A + mB -> (m + 1)B, and a linear decay B -> C, where C is an inert product. The special case of m = 2 is the much studied Gray-Scott model, but without feeding. We prove existence of multiple traveling waves which have distinctive number of local maxima or peaks. It shows a new and very distinctive feature of Gray-Scott type of models in generating rich and structurally different traveling pulses than related models in literature such as isothermal autocatalysis without decay, or a bio-reactor model with isothermal autocatalysis of order m + 1 with m-th order of decay.

引用

页码：154 / +

页数：19

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