Chin. Phys. B ›› 2013, Vol. 22 ›› Issue (12): 120503-120503.doi: 10.1088/1674-1056/22/12/120503

• GENERAL • 上一篇    下一篇

Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

王慧娟, 王永杰, 任芝   

  1. School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
  • 收稿日期:2013-07-27 修回日期:2013-09-22 出版日期:2013-10-25 发布日期:2013-10-25
  • 基金资助:
    Project supported by the National Nature Science Foundation of China (Grant No. 11205044) and the Fundamental Research Funds for the Central Universities (Grant No. 10ML40).

Control of the patterns by using time-delayed feedback near the codimension-three Turing–Hopf–Wave bifurcations

Wang Hui-Juan (王慧娟), Wang Yong-Jie (王永杰), Ren Zhi (任芝)   

  1. School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
  • Received:2013-07-27 Revised:2013-09-22 Online:2013-10-25 Published:2013-10-25
  • Contact: Wang Hui-Juan E-mail:whuijuanmail@126.com
  • Supported by:
    Project supported by the National Nature Science Foundation of China (Grant No. 11205044) and the Fundamental Research Funds for the Central Universities (Grant No. 10ML40).

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摘要： Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional (2D) numerical simulations.

关键词: pattern formation, reaction diffusion system, time-delayed feedback

Abstract: Control of the spatiotemporal patterns near the codimension-three Turing–Hopf–Wave bifurcations is studied by using time-delayed feedback in a three-variable Brusselator model. Linear stability analysis of the system shows that the competition among the Turing-, Hopf- and Wave-modes, the wavenumber, and the oscillation frequency of patterns can be controlled by changing the feedback parameters. The role of the feedback intensity Pu played on controlling the pattern competition is equivalent to that of Pw, but opposite to that of Pv. The role of the feedback intensity Pu played on controlling the wavenumber and oscillation frequency of patterns is equivalent to that of Pv, but opposite to that of Pw. When the intensities of feedback are applied equally, changing the delayed time could not alter the competition among these modes, however, it can control the oscillation frequency of patterns. The analytical results are verified by two-dimensional (2D) numerical simulations.

Key words: pattern formation, reaction diffusion system, time-delayed feedback

中图分类号:  (Nonlinear dynamics and chaos)

  • 05.45.-a
82.40.Ck (Pattern formation in reactions with diffusion, flow and heat transfer) 47.54.-r (Pattern selection; pattern formation)