中国物理B ›› 2016, Vol. 25 ›› Issue (10): 104702-104702.doi: 10.1088/1674-1056/25/10/104702

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Pattern formation in superdiffusion Oregonator model

Fan Feng(冯帆), Jia Yan(闫佳), Fu-Cheng Liu(刘富成), Ya-Feng He(贺亚峰)   

  1. Hebei Key Laboratory of Optic-electronic Information Materials, College of Physics Science and Technology, Hebei University, Baoding 071002, China
  • 收稿日期:2016-03-02 修回日期:2016-06-10 出版日期:2016-10-05 发布日期:2016-10-05
  • 通讯作者: Ya-Feng He E-mail:heyf@hbu.edu.cn
  • 基金资助:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

Pattern formation in superdiffusion Oregonator model

Fan Feng(冯帆), Jia Yan(闫佳), Fu-Cheng Liu(刘富成), Ya-Feng He(贺亚峰)   

  1. Hebei Key Laboratory of Optic-electronic Information Materials, College of Physics Science and Technology, Hebei University, Baoding 071002, China
  • Received:2016-03-02 Revised:2016-06-10 Online:2016-10-05 Published:2016-10-05
  • Contact: Ya-Feng He E-mail:heyf@hbu.edu.cn
  • Supported by:

    Project supported by the National Natural Science Foundation of China (Grant Nos. 11205044 and 11405042), the Research Foundation of Education Bureau of Hebei Province, China (Grant Nos. Y2012009 and ZD2015025), the Program for Young Principal Investigators of Hebei Province, China, and the Midwest Universities Comprehensive Strength Promotion Project.

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摘要：

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.

关键词: pattern formation, reaction diffusion system, anomalous diffusion

Abstract:

Pattern formations in an Oregonator model with superdiffusion are studied in two-dimensional (2D) numerical simulations. Stability analyses are performed by applying Fourier and Laplace transforms to the space fractional reaction-diffusion systems. Antispiral, stable turing patterns, and travelling patterns are observed by changing the diffusion index of the activator. Analyses of Floquet multipliers show that the limit cycle solution loses stability at the wave number of the primitive vector of the travelling hexagonal pattern. We also observed a transition between antispiral and spiral by changing the diffusion index of the inhibitor.

Key words: pattern formation, reaction diffusion system, anomalous diffusion

中图分类号:  (Pattern selection; pattern formation)

  • 47.54.-r
05.45.-a (Nonlinear dynamics and chaos) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)