Phase portraits and bifurcation diagram of the Gray-Scott model

被引：5

作者：

Chen, Ting ^{[1
]}

Li, Shimin ^{[1
]}

Llibre, Jaume ^{[2
]}

机构：

[1] Guangdong Univ Finance & Econ, Sch Stat & Math, Guangzhou 510320, Peoples R China

[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Catalonia, Spain

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 496卷 / 02期

基金：

中国国家自然科学基金; 欧盟地平线“2020”;

关键词：

Gray-Scott model; Cubic polynomial system; Phase portraits; Bifurcation diagram; Hopf bifurcation; HAMILTONIAN-SYSTEMS; LIMIT-CYCLES; CENTERS;

D O I：

10.1016/j.jmaa.2020.124840

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a complete classification of the phase portraits in the Poincare disk for the cubic polynomial systems (x) over dot = 1 - x - axy(2), (y) over dot = -by + axy(2), in R-2 according with the values of its two parameters a and b. These differential systems correspond to the Gray-Scott model. Moreover we provide the bifurcation diagram in the parameter plane (a, b) of these systems. (C) 2020 Elsevier Inc. All rights reserved.

引用

页数：27

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