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Discretized locally active memristor and application in logarithmic map

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Abstract

Compared with continuous memristor, discrete memristor is more suitable for the application of memristor in discrete system. However, discrete memristor has not been fully appreciated. In this paper, a discrete memristor is obtained by discretizing continuous memristor based on the rectangular pulse discrete sampling method (RPDSM), and it satisfies the definition of generalized memristor by identifying fingerprint characteristics. The perfect matching of the v–i curves for appropriate sampling period further confirms the correctness of discretization result. Power-off plot and DC V–I plot are utilized to dissect the volatility and local activity of the memristor. Then, a new discrete memristive map, called DLAM-Log map for short, is constructed by coupling the discretized locally active memristor and logarithmic function. It shows that the DLAM-Log map can generate complex dynamics such as robust chaos, coexisting multiple attractors and some special transient dynamics. Finally, a practical modulation scheme of signal amplitude and functional type is proposed by introducing control function into the DLAM-Log map. The feasibility of the modulation scheme is theoretically interpreted and numerically validated, which shows potential significance in chaos-based information engineering.

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Funding

This work was supported by Hunan Provincial Natural Science Foundation of China (Nos. 2019JJ40109, 2020JJ4337); 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).

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Authors and Affiliations

  1. Hunan Institute of Science and Technology, College of Physics and Electronics, Yueyang, 414006, China

    Haodong Li, Chunlai Li & Jianrong Du

  2. School of Computer Science & School of Cyberspace Science, Xiangtan University, Xiangtan, 411105, China

    Chunlai Li

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  1. Haodong Li
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Correspondence to Chunlai Li.

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Li, H., Li, C. & Du, J. Discretized locally active memristor and application in logarithmic map. Nonlinear Dyn 111, 2895–2915 (2023). https://doi.org/10.1007/s11071-022-07955-w

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