中国物理B ›› 2008, Vol. 17 ›› Issue (11): 4047-4055.doi: 10.1088/1674-1056/17/11/018

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Formation and instability of spiral wave induced by Gaussian coloured noise

马 军1, 张国勇2, 甘正宁3, 陈 勇4   

  1. (1)Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China; (2)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; (3)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;College of Electronic and Information Engineering, Changsha University of Science $\&$ Technology, Changsha 410076, China; (4)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China;Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2008-04-03 修回日期:2008-04-17 出版日期:2008-11-20 发布日期:2008-11-20
  • 基金资助:
    Project supported partially by National Science Foundation of China (Grant No 10305005) and by the Fundamental Research Fund for Physics and Mathematic of Lanzhou University of China.

Formation and instability of spiral wave induced by Gaussian coloured noise

Gan Zheng-Ning(甘正宁)ab, Ma Jun (马军)c,  Zhang Guo-Yong(张国勇)a, Chen Yong (陈勇)ad   

  1. a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; b College of Electronic and Information Engineering, Changsha University of Science & Technology, Changsha 410076, China; c Department of Physics, Lanzhou University of Technology, Lanzhou 730050, China; d Key Laboratory for Magnetism and Magnetic Materials of the Ministry of Education, Lanzhou University, Lanzhou 730000, China
  • Received:2008-04-03 Revised:2008-04-17 Online:2008-11-20 Published:2008-11-20
  • Supported by:
    Project supported partially by National Science Foundation of China (Grant No 10305005) and by the Fundamental Research Fund for Physics and Mathematic of Lanzhou University of China.

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摘要： In this paper, we studied the effect of Gaussian coloured noise on the formation and instability of spiral waves described by one class of modified FitzHugh--Nagumo equation. It was found that Gaussian coloured noise plays a constructive role in the formation, transition and instability of spiral wave. Too weak or too strong noise may act against the formation of spiral waves. At a certain noise level, spiral wave is maintained in a medium, in which spiral wave cannot be observed in the absence of the noise. It is difficult to make a stable spiral wave into unstable state by Gaussian coloured noise, unless the noise level is very high. The parameter regions of Gaussian coloured noise for spiral forming and spiral instability were given and discussed with numerical simulations.

关键词: spiral wave, FitzHugh--Nagumo model, Gaussian coloured noise

Abstract: In this paper, we studied the effect of Gaussian coloured noise on the formation and instability of spiral waves described by one class of modified FitzHugh--Nagumo equation. It was found that Gaussian coloured noise plays a constructive role in the formation, transition and instability of spiral wave. Too weak or too strong noise may act against the formation of spiral waves. At a certain noise level, spiral wave is maintained in a medium, in which spiral wave cannot be observed in the absence of the noise. It is difficult to make a stable spiral wave into unstable state by Gaussian coloured noise, unless the noise level is very high. The parameter regions of Gaussian coloured noise for spiral forming and spiral instability were given and discussed with numerical simulations.

Key words: spiral wave, FitzHugh--Nagumo model, Gaussian coloured noise

中图分类号:  (Noise)

  • 05.40.Ca
05.45.-a (Nonlinear dynamics and chaos)