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Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map

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Abstract

Compared with continuous-time memristor (CM), discrete memristor (DM) has not been received adequate attention. In this paper, a new n-dimensional generalized DM model is proposed based on the discrete theory. Two 2-D discrete mathematical models satisfying the three fingerprints characteristics of memristors are designed. Applying the mathematical model into the Sine map yields a new hyperchaotic map called discrete memristor-based Sine (DM-S) map. The DM-S map has a line of fixed points, and its dynamical behaviors including nonparametric bifurcation and hyperchaos are explored by phase diagrams, bifurcation diagrams, and Lyapunov exponent spectrums. The i–v characteristics of the DM and the attractors of the DM-S map are implemented by digital signal processor. In addition, the sequences of map are tested by using SP800-22 NIST software.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 61801271, 61973200, 91848206 and 61771176), Natural Science Foundation of Shandong Province (Grant No. ZR2019BF007), Qingdao Science and Technology Plan Project (Grant No. 19-6-2-9-cg). This work was also supported by the Taishan Scholar Project of Shandong Province of China.

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  1. School of Automation and Electrical Engineering, Shandong University of Science and Technology, Qingdao, 266590, China

    Yue Deng & Yuxia Li

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  1. Yue Deng
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  2. Yuxia Li
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Correspondence to Yuxia Li.

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Deng, Y., Li, Y. Nonparametric bifurcation mechanism in 2-D hyperchaotic discrete memristor-based map. Nonlinear Dyn 104, 4601–4614 (2021). https://doi.org/10.1007/s11071-021-06544-7

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