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Control spiral and multi-spiral wave in the complex Ginzburg–Landau equation

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  • Ma, Jun
  • Gao, Ji-Hua
  • Wang, Chun-Ni
  • Su, Jun-Yan

Abstract

In this letter, scheme is proposed to suppress the spiral wave and multi-spiral waves in the complex Ginzburg–Landau equation (CGLE) under a local feedback control, which the perturbation is imposed on a small square area about 3×3 grids in the center of the media under periodical boundary conditions and 5×5 grids in the boundary of the media under no-flux conditions. Starting from random and/or perpendicular-gradient initial conditions, and the periodical boundary condition and/or no-flux boundary condition is in consideration, respectively. The numerical simulation results show that a target wave appears as the feedback began to work and the spiral and multi-spiral waves are overcome by the new generated target wave, furthermore, it confirms its effectiveness even if the spatiotemporal noise is introduced into the whole media.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:38:y:2008:i:2:p:521-530
    DOI: 10.1016/j.chaos.2006.11.039
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    Cited by:

    1. 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).
    2. 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).
    3. 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.
    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.

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