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A necessary and sufficient condition for anti-synchronization of a class of chaotic systems

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Abstract

We investigate anti-synchronization for a class of chaotic systems; and propose a necessary and sufficient condition with which one can determine whether anti-synchronization of a given chaotic system can be realized or not. This condition is general and when satisfied would guarantee the simultaneous synchronization and anti-synchronization of a master–slave chaotic system. Furthermore, by extending the existing adaptive control method, an adaptive control algorithm has been designed to achieve the anti-synchronization. The efficiency and effectiveness of this method have been verified with several simulations using three different chaotic and hyperchaotic systems.

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Acknowledgments

This work was supported by National Natural Science Foundation of China (61304133, 61305130, 61374074), China Postdoctoral Science Foundation funded Project (2013M541915, 2013M541912, 2014T70638) and the Scientific Research Foundation of Shandong province Outstanding Young Scientist Award (BS2013SF023). The work of UEV is supported by the Royal Society of London through their Newton International Fellowship Alumni scheme.

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Authors and Affiliations

  1. School of Science, Qilu University of Technology, Jinan, 250353, People’s Republic of China

    Ling Ren & Rongwei Guo

  2. Department of Physical Sciences, Redeemer’s University, Redemption City, Nigeria

    U. E. Vincent

  3. Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom

    U. E. Vincent

Authors
  1. Ling Ren
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  2. Rongwei Guo
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  3. U. E. Vincent
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Correspondence to U. E. Vincent.

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Ren, L., Guo, R. & Vincent, U.E. A necessary and sufficient condition for anti-synchronization of a class of chaotic systems. Int. J. Dynam. Control 5, 1252–1261 (2017). https://doi.org/10.1007/s40435-016-0278-2

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  • DOI: https://doi.org/10.1007/s40435-016-0278-2

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