中国物理B ›› 2007, Vol. 16 ›› Issue (4): 1159-1166.doi: 10.1088/1009-1963/16/4/051

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Breakup of spiral wave under different boundary conditions

王光瑞1, 陈式刚1, 赵英奎2   

  1. (1)Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China; (2)Graduate School of China Academy of Engineering Physics, Beijing 100088, China;Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • 收稿日期:2006-07-11 修回日期:2006-11-08 出版日期:2007-04-20 发布日期:2007-04-20
  • 基金资助:
    Project supported by the Major Program of the National Natural Science Foundation for (Grant No 10335010) and the National Natural Science Foundation--the Science Foundation of China Academy of Engineering Physics (NSAF) (Grant No 10576005).

Breakup of spiral wave under different boundary conditions

Zhao Ying-Kui(赵英奎)a)b)†, Wang Guang-Rui(王光瑞)b), and Chen Shi-Gang (陈式刚)b)   

  1. a Graduate School of China Academy of Engineering Physics, Beijing 100088, China; b Center for Nonlinear Studies, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
  • Received:2006-07-11 Revised:2006-11-08 Online:2007-04-20 Published:2007-04-20
  • Supported by:
    Project supported by the Major Program of the National Natural Science Foundation for (Grant No 10335010) and the National Natural Science Foundation--the Science Foundation of China Academy of Engineering Physics (NSAF) (Grant No 10576005).

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摘要： In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter \varepsilon is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of \varepsilon.

关键词: spiral, breakup, boundary, reaction-diffusion

Abstract: In this paper, we investigate the breakup of spiral wave under no-flux, periodic and Dirichlet boundary conditions respectively. When the parameter $\varepsilon$ is close to a critical value for Doppler-induced wave breakup, the instability of the system caused by the boundary effect occurs in the last two cases, resulting in the breakup of spiral wave near the boundary. With our defined average order measure of spiral wave (AOMSW), we quantify the degree of order of the system when the boundary-induced breakup of spiral wave happens. By analysing the AOMSW and outer diameter R of the spiral tip orbit, it is easy to find that this boundary effect is correlated with large values of R, especially under the Dirichlet boundary condition. This correlation is nonlinear, so the AOMSW sometimes oscillates with the variation of $\varepsilon$.

Key words: spiral, breakup, boundary, reaction-diffusion

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
05.65.+b (Self-organized systems)