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Spiral waves in excitable media due to noise and periodic forcing

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  • Yuan, Guoyong
  • Xu, Lin
  • Xu, Aiguo
  • Wang, Guangrui
  • Yang, Shiping

Abstract

We investigate the jointly driven effects of external periodic forcing and Gaussian white noise on meandering spiral waves in excitable media with FitzHugh–Nagumo local dynamics. Interesting phenomena resulted from various forcing periods are found, for example, piece-wise line drift, intermittent straight-line drift and so on. We also observe new type of breakup of spiral wave between entrainment bands with 1:1 and 2:1. It is believed that the occurrence of the new type is relevant to the appearance of local bidirectional propagation window. There exist optimized noise intensities which can induce the broadest entrainments and Arnold tongues. Such a phenomenon is referred to as stochastic resonance. It is also observed that the noise makes significant effects on the spiral wave with straight-line drift. Via the tip Fourier spectrum, the varying of tip motion with external periods on the resonance band is interpreted.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:9:p:728-738
    DOI: 10.1016/j.chaos.2011.06.013
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    References listed on IDEAS

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    1. Perc, Matjaž, 2007. "Effects of small-world connectivity on noise-induced temporal and spatial order in neural media," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 280-291.
    2. 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.
    3. Ma, Jun & Wang, Chun-Ni & Li, Yan-Long & Li, Shi-Rong, 2007. "Suppression of spiral waves in light-sensitive media using chaotic signal modulated scheme," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 965-970.
    4. G. Y. Yuan & S. G. Chen & S. P. Yang, 2007. "Eliminating spiral waves and spatiotemporal chaos using feedback signal," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 58(3), pages 331-336, August.
    5. Perc, Matjaž, 2007. "Spatial coherence resonance in neuronal media with discrete local dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 64-69.
    6. Sándor Kádár & Jichang Wang & Kenneth Showalter, 1998. "Noise-supported travelling waves in sub-excitable media," Nature, Nature, vol. 391(6669), pages 770-772, February.
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    Cited by:

    1. Wang, Xueli & Yuan, Guoyong & Liu, Jun & Wang, Guangrui, 2020. "Control of spiral drift by using feedback signals from a circular measuring domain in oscillatory media," Applied Mathematics and Computation, Elsevier, vol. 368(C).
    2. Hu, Yipeng & Ding, Qianming & Wu, Yong & Jia, Ya, 2023. "Polarized electric field-induced drift of spiral waves in discontinuous cardiac media," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).

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