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.
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页数：27
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