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Impulsive control and synchronization of spatiotemporal chaos

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  • Khadra, Anmar
  • Liu, Xinzhi
  • Shen, Xuemin

Abstract

The impulsive control of spatiotemporal chaos of a particular type of non-linear partial differential equations has been investigated. A criterion for the solutions of these partial differential equations to be equi-attractive in the large is determined and an estimate for the basin of attraction is given in terms of the impulse durations and the magnitude of the impulses. Extending these results to impulsively synchronize spatiotemporal chaos of the same type of partial differential equations is explored. A proof for the existence of a certain kind of impulses for synchronization such that the error dynamics is equi-attractive in the large, is established. A comparison of the developed theoretical model with other existent numerical models available in the literature has been studied. Several simulation results are given to confirm the theoretical results. Moreover, an investigation of the Lyapunov exponents of the error dynamics between impulsively synchronized spatiotemporal chaotic systems, is done to further confirm the theoretical results.

Suggested Citation

  • Khadra, Anmar & Liu, Xinzhi & Shen, Xuemin, 2005. "Impulsive control and synchronization of spatiotemporal chaos," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 615-636.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:615-636
    DOI: 10.1016/j.chaos.2004.01.020
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    Citations

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    Cited by:

    1. Zhang, Yinping & Sun, Jitao, 2009. "Impulsive robust fault-tolerant feedback control for chaotic Lur’e systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1440-1446.
    2. Zheng, Yongai & Chen, Guanrong, 2009. "Fuzzy impulsive control of chaotic systems based on TS fuzzy model," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 2002-2011.
    3. Du, Shengzhi & van Wyk, Barend J. & Qi, Guoyuan & Tu, Chunling, 2009. "Chaotic system synchronization with an unknown master model using a hybrid HOD active control approach," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1900-1913.
    4. Litak, G. & Borowiec, M. & Ali, M. & Saha, L.M. & Friswell, M.I., 2007. "Pulsive feedback control of a quarter car model forced by a road profile," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1672-1676.
    5. Feng, Xiu-Qin & Shen, Ke, 2008. "Controlling hyperchaos and periodic synchronization in DOPO with parameter modulated by an external periodic signal," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 506-511.

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