IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i3p1331-1339.html
   My bibliography  Save this article

Suppression of spiral wave and turbulence by using amplitude restriction of variable in a local square area

Author

Listed:
  • Ma, Jun
  • Jia, Ya
  • Yi, Ming
  • Tang, Jun
  • Xia, Ya-Feng

Abstract

In this paper, a new scheme is proposed to eliminate the useless spiral wave and turbulence in the excitable media. The activator amplitudes of few sites in the media are sampled and restricted within the appropriate thresholds. At first, the local control is imposed on the center of the media, and then the local control is introduced into the left border in the media. The numerical simulation results confirm that the whole media can reach homogeneous within few time units even if the spatiotemporal noise is imposed on the whole media. To check the model independence of this scheme, the scheme is used to remove the spiral wave in the Fitzhugh–Nagumo model firstly. In our numerical simulation, the whole system is discretized into 400×400 sites. Then the scheme is used to eliminate the stable rotating spiral wave, meandering spiral and spiral turbulence in the modified Fitzhugh–Nagumo model, respectively. Finally, this scheme is used to remove the stable rotating spiral wave in the Belousov–Zhabotinsky (BZ) reaction. All the results just confirm its effectiveness to eliminate the spiral wave and turbulence. The criterion for thresholds selection is also discussed in the end of this paper.

Suggested Citation

  • Ma, Jun & Jia, Ya & Yi, Ming & Tang, Jun & Xia, Ya-Feng, 2009. "Suppression of spiral wave and turbulence by using amplitude restriction of variable in a local square area," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1331-1339.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1331-1339
    DOI: 10.1016/j.chaos.2008.05.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077908002567
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2008.05.014?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jun, Ma & Yan-Long, Li & Jin-Long, Jiang & Yan-Jun, Liu & Chun-Ni, Wang, 2006. "Evolution of spiral waves subjected to parameter modulation under chaotic signal," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(2), pages 387-392.
    2. Duan, Wen-shan, 2006. "3+1 dimensional envelop waves and its stability in magnetized dusty plasma," Chaos, Solitons & Fractals, Elsevier, vol. 27(4), pages 926-929.
    3. Yu, Simin & Tang, Wallace K.S., 2009. "Generation of n×m-scroll attractors in a two-port RCL network with hysteresis circuits," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 821-830.
    4. Sriram, K., 2006. "Effects of positive electrical feedback in the oscillating Belousov–Zhabotinsky reaction: Experiments and simulations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1055-1066.
    5. Ma, Jun & Gao, Ji-Hua & Wang, Chun-Ni & Su, Jun-Yan, 2008. "Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 521-530.
    6. Lin, Mai-mai & Duan, Wen-shan, 2007. "Dust acoustic solitary waves in a dusty plasmas with nonthermal ions," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1189-1196.
    7. Xue, Ju-Kui & Zhang, Li-Ping, 2007. "Non-linear waves in complex plasma," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 592-597.
    8. Tang, Rong-An & Xue, Ju-Kui, 2006. "Chaotic synchronization by replacing nonlinear terms with signals," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 228-235.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. El-Nabulsi, Rami Ahmad & Anukool, Waranont, 2024. "Spiral waves in fractal dimensions and their elimination in λ − ω systems with less damaging intervention," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. Ma, Jun & Xu, Ying & Wang, Chunni & Jin, Wuyin, 2016. "Pattern selection and self-organization induced by random boundary initial values in a neuronal network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 586-594.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pakzad, Hamid Reza & Javidan, Kurosh, 2009. "Solitary waves in dusty plasmas with variable dust charge and two temperature ions," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2904-2913.
    2. Tribeche, Mouloud & Younsi, Smain & Zerguini, Taha Houssine, 2009. "Nonlinear solitary oscillations in a varying charge dusty plasma in the presence of nonisothermal trapped electrons," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1277-1283.
    3. Lei Fu & Hongwei Yang, 2019. "An Application of (3+1)-Dimensional Time-Space Fractional ZK Model to Analyze the Complex Dust Acoustic Waves," Complexity, Hindawi, vol. 2019, pages 1-15, August.
    4. Yuan, Guoyong & Xu, Lin & Xu, Aiguo & Wang, Guangrui & Yang, Shiping, 2011. "Spiral waves in excitable media due to noise and periodic forcing," Chaos, Solitons & Fractals, Elsevier, vol. 44(9), pages 728-738.
    5. Kaur, Harvinder & Gill, Tarsem Singh & Saini, Nareshpal Singh, 2009. "Characteristics of some nonlinear coherent wave structures in a collisionless weakly relativistic plasma with nonthermal electrons," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1638-1645.
    6. Zhang, Chaoxia & Yu, Simin, 2011. "Generation of multi-wing chaotic attractor in fractional order system," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 845-850.
    7. Yu, Simin & Tang, Wallace K.S., 2009. "Tetrapterous butterfly attractors in modified Lorenz systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1740-1749.
    8. Zhang, Yiling & Yuan, Guoyong & Liu, Jun & Shi, Jifang & Wang, Guangrui & Chen, Shaoying, 2023. "Spiral dynamics in oscillatory bilayer systems with an inhomogeneous inter-layer coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).
    9. Yuan, Guoyong & Liu, Pengwei & Shi, Jifang & Wang, Guangrui, 2023. "Dynamics and control of spiral waves under feedback derived from a moving measuring point," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:41:y:2009:i:3:p:1331-1339. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.