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Self-reproducing dynamics in a two-dimensional discrete map

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Abstract

This paper mainly explores the self-reproducing dynamics in discrete-time system by constructing a two-dimension map with infinitely many fixed points. Theoretical analysis shows that the attractor of the map can not only be non-destructively reproduced by the initial values of all state variables along all axis directions, but can also be non-destructively reproduced by the parameter along all axis directions. The numerical simulations of bifurcation diagram, Lyapunov exponent, phase portrait and iterative sequence are carried out to further confirm the theoretical results. The self-reproducing behavior of different type of attractors and the corresponding iterative sequences are also confirmed by the experimental measurements performed on the DSP-based platform. This map is especially suitable for chaos-based engineering applications since the offset can be periodically switched by the initial condition and parameter on the premise of keeping robust dynamical behavior.

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Acknowledgements

This work was supported in part by Hunan Provincial Natural Science Foundation of China (Nos. 2019JJ40109, 2020JJ4337); Research Foundation of Education Bureau of Hunan Province of China (No. 18A314); Science and Technology Program of Hunan Province (No. 2019TP1014); Science and Research Creative Team of Hunan Institute of Science and Technology (No. 2019-TD-10); Natural Science Foundation of China (No. 61901530); research and innovation project of the graduate students of Hunan Institute of Science and Technology (No. YCX2020 A336).

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Authors and Affiliations

  1. Key Laboratory of Hunan Province on Information Photonics and Freespace Optical Communications, Hunan Institute of Science and Technology, Yueyang, 414006, China

    Chunlai Li, Zhen Chen, Xuanbing Yang, Yongyan Yang & Jianrong Du

  2. School of Physics and Electronics, Central South University, Changsha, 410083, China

    Shaobo He

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  1. Chunlai Li
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  2. Zhen Chen
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Contributions

Paper conception: CL. Experimental conception and design: CL, XY. Experiment implementation: XY, JD. Software simulation: ZC, YY. Data analysis: SH. Paper writing: CL.

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Correspondence to Chunlai Li.

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Li, C., Chen, Z., Yang, X. et al. Self-reproducing dynamics in a two-dimensional discrete map. Eur. Phys. J. Spec. Top. 230, 1959–1970 (2021). https://doi.org/10.1140/epjs/s11734-021-00182-1

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