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A non-degenerate m-dimensional integer domain chaotic map model over GF(2n)

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Abstract

To solve the problem of dynamic degradation over finite precision platform of chaotic map, we proposed a non-degenerate m-dimensional (m ≥ 2) integer domain chaotic map (mD-IDCM) model over GF(2n), which can be applied to construct arbitrary non-degenerate m-dimensional integer domain chaotic map with m positive Lyapunov exponents. Then, we proved the strong connectivity of state transition graphs of mD-IDCM, and further proved that the mD-IDCM is chaotic in the sense of Devaney. In addition, we proved the boundedness of Lyapunov exponents. To verify the effectiveness of mD-IDCM, we instantiated it to construct two maps and analyzed their dynamical behavior. Experimental results indicated that the integer domain chaotic maps constructed by mD-IDCM have ergodicity within a sufficient larger chaotic range and exhibit complex dynamic behavior.

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Funding

This research is supported by the Natural Science Foundation of Shandong Province (No. ZR2022MF232), and the Teaching and Research Program of University of Jinan (No. J2203).

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

    Dongya Xu & Hongjun Liu

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  1. Dongya Xu
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  2. Hongjun Liu
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Correspondence to Hongjun Liu.

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Xu, D., Liu, H. A non-degenerate m-dimensional integer domain chaotic map model over GF(2n). Nonlinear Dyn (2024). https://doi.org/10.1007/s11071-024-09517-8

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