Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

doi:10.1088/1674-1056/24/4/048201

›› 2015, Vol. 24 ›› Issue (4): 48201-048201.doi: 10.1088/1674-1056/24/4/048201

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

李新政^a, 白占国^a, 李燕^a, 贺亚峰^b, 赵昆^a

a College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China;
b College of Physics Science and Technology, Hebei University, Baoding 071002, China

收稿日期:2014-10-24 修回日期:2014-11-25 出版日期:2015-04-05 发布日期:2015-04-05
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11247242), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51201057), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014208171).

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

Li Xin-Zheng (李新政)^a, Bai Zhan-Guo (白占国)^a, Li Yan (李燕)^a, He Ya-Feng (贺亚峰)^b, Zhao Kun (赵昆)^a

a College of Sciences, Hebei University of Science and Technology, Shijiazhuang 050018, China;
b College of Physics Science and Technology, Hebei University, Baoding 071002, China

Received:2014-10-24 Revised:2014-11-25 Online:2015-04-05 Published:2015-04-05
Contact: Bai Zhan-Guo E-mail:baizg2006163@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11247242), the Young Scientists Fund of the National Natural Science Foundation of China (Grant No. 51201057), and the Natural Science Foundation of Hebei Province, China (Grant No. A2014208171).

摘要/Abstract

摘要： The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.

关键词: Brusselator model, pattern formation, Turing mode, instability

Abstract: The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.

Key words: Brusselator model, pattern formation, Turing mode, instability

中图分类号: (Oscillations, chaos, and bifurcations)

82.40.Bj

05.45.-a (Nonlinear dynamics and chaos) 47.54.-r (Pattern selection; pattern formation)

李新政, 白占国, 李燕, 贺亚峰, 赵昆. Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system[J]. , 2015, 24(4): 48201-048201.

Li Xin-Zheng (李新政), Bai Zhan-Guo (白占国), Li Yan (李燕), He Ya-Feng (贺亚峰), Zhao Kun (赵昆). Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system[J]. Chin. Phys. B, 2015, 24(4): 48201-048201.

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Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

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