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Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension

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Abstract

Ultimate bound estimation of chaotic systems is a difficult yet interesting mathematical question. At present, explicit ultimate bound sets can be analytically obtained only for some special chaotic systems, and few results are known for hyper-chaotic ones. In this paper, through the Lagrange multiplier method and set operations, one derives two kinds of explicit ultimate bound sets for a novel hyperchaotic system. Based on the estimated result and optimization method, one further estimates the Hausdorff dimension of the hyperchaotic attractor. Numerical simulations show the effectiveness and correctness of the conclusions. The investigations enrich the related results for the hyperchaotic systems, and provide support for the assertion: hyperchaotic systems are ultimately bounded.

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Acknowledgements

This work was supported by the Science Foundation of Henan University under Grants 2012YBZR007, and also partly supported by the National Natural Science Foundation of China under Grants 60804039, 60974081, 11271295, and 60821091. This work was also partly supported by the Science and Technology Research Projects of Hubei Provincial Department of Education under Grants: D20131602.

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Authors and Affiliations

  1. School of Mathematics and Information Sciences, Henan University, Kaifeng, 475004, China

    Pei Wang & Yuhuan Zhang

  2. LSC, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, P.R. China

    Shaolin Tan

  3. School of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073, P.R. China

    Li Wan

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  1. Pei Wang
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  2. Yuhuan Zhang
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  3. Shaolin Tan
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  4. Li Wan
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Correspondence to Pei Wang.

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Wang, P., Zhang, Y., Tan, S. et al. Explicit ultimate bound sets of a new hyperchaotic system and its application in estimating the Hausdorff dimension. Nonlinear Dyn 74, 133–142 (2013). https://doi.org/10.1007/s11071-013-0953-1

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  • DOI: https://doi.org/10.1007/s11071-013-0953-1

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