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An answer to the open problem of \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization for time-delayed chaotic systems

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Abstract

In this paper, we deal with the open problem of \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization for time-delayed chaotic systems with external disturbance. To date, a control scheme has been proposed to synchronize chaotic systems without time delay, but no solution exists for the case when chaotic systems have time delay. For the first time, in this paper, we prove that a new criterion for the \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization of time-delayed chaotic systems exists.

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Author notes

  1. Choon Ki Ahn

    Present address: Seoul National University of Science & Technology, Room 717, Frontier Bldg., 172 Gongneung 2-dong, Nowon-gu, 139-743, Seoul, Korea

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    1. Choon Ki Ahn
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    Correspondence to Choon Ki Ahn.

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    Ahn, C.K. An answer to the open problem of \(\mathcal{L}_2 - \mathcal{L}_\infty\) synchronization for time-delayed chaotic systems. Eur. Phys. J. Plus 127, 22 (2012). https://doi.org/10.1140/epjp/i2012-12022-2

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    • DOI: https://doi.org/10.1140/epjp/i2012-12022-2

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