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Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type
Joint Authors
Gu, Lianchao
Gong, Peiliang
Wang, Hongqing
Source
Discrete Dynamics in Nature and Society
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-01-22
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
The reaction diffusion system is one of the important models to describe the objective world.
It is of great guiding importance for people to understand the real world by studying the Turing patterns of the reaction diffusion system changing with the system parameters.
Therefore, in this paper, we study Gierer–Meinhardt model of the Depletion type which is a representative model in the reaction diffusion system.
Firstly, we investigate the stability of the equilibrium and the Hopf bifurcation of the system.
The result shows that equilibrium experiences a Hopf bifurcation in certain conditions and the Hopf bifurcation of this system is supercritical.
Then, we analyze the system equation with the diffusion and study the impacts of diffusion coefficients on the stability of equilibrium and the limit cycle of system.
Finally, we perform the numerical simulations for the obtained results which show that the Turing patterns are either spot or stripe patterns.
American Psychological Association (APA)
Gu, Lianchao& Gong, Peiliang& Wang, Hongqing. 2020. Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type. Discrete Dynamics in Nature and Society،Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153145
Modern Language Association (MLA)
Gu, Lianchao…[et al.]. Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type. Discrete Dynamics in Nature and Society No. 2020 (2020), pp.1-10.
https://search.emarefa.net/detail/BIM-1153145
American Medical Association (AMA)
Gu, Lianchao& Gong, Peiliang& Wang, Hongqing. Hopf Bifurcation and Turing Instability Analysis for the Gierer–Meinhardt Model of the Depletion Type. Discrete Dynamics in Nature and Society. 2020. Vol. 2020, no. 2020, pp.1-10.
https://search.emarefa.net/detail/BIM-1153145
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1153145