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Spatial chaos on surface and its associated bifurcation and Feigenbaum problem

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Abstract

The qualitative theory of nonlinear spatial dynamical systems has attracted increasing attention recently. In particular, we have studied construction of spatial periodic orbits, dynamical behaviors of spatial chaos in the sense of Li–Yorke–Marotto, spatial Lyapunov exponents, control and generalized synchronization of spatial chaotic systems. In this paper, we apply a special mathematical transform to obtain spatial chaos on surface and its associated bifurcation and Feigenbaum problem. The 2D Logistic system is used for illustration. In addition, we also illustrate the difference in essence about chaos on surface as high-dimensional spatial system and dimension in phase space and we also analyze the parallel and different characters of theory system between 1D and 2D Logistic system.

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Acknowledgments

Thank you for reviewer’s valuable suggestions. The work was supported by the Natural Science Foundation Project (Nos.31301080, 61273088 and 10971120), National Key Technology Support Program (No. 2015BAF13B00) and the Open Project of State Key Laboratory of Crop Biology (No. 2013KF10).

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Authors and Affiliations

  1. College of Control Science and Engineering, Shandong University, Jinan, 250061, China

    Shutang Liu & Jian Liu

  2. College of Mechanical and Electronic Engineering, Shandong Agricultural University, Taian, 271018, China

    Ping Liu & Leyuan Wang

  3. College of Engineering, Peking University, Beijing, 100871, China

    Ping Liu

  4. School of Mathematical Sciences, University of Jinan, Jinan Shandong, 250022, China

    Jian Liu

Authors
  1. Shutang Liu
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  2. Ping Liu
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  3. Jian Liu
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  4. Leyuan Wang
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Correspondence to Ping Liu.

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Liu, S., Liu, P., Liu, J. et al. Spatial chaos on surface and its associated bifurcation and Feigenbaum problem. Nonlinear Dyn 81, 283–298 (2015). https://doi.org/10.1007/s11071-015-1991-7

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  • DOI: https://doi.org/10.1007/s11071-015-1991-7

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