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Discrete fracmemristor model with the window function and its application in Logistic map

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Abstract

In recent years, the mathematical model of memristor has attracted extensive attention from researchers, but the boundary effect of the memristor model is rarely considered. A memristor with the window function is proposed in this paper. First, the boundary effect of the device is ignored by the conventional memristive model, but the memristor model with the window function can effectively solve this problem. Then, based on the fractional difference theory, a discrete fractional mathematical model of memristor with the window function is studied. Meanwhile, the corresponding three memristor characteristics are verified for this model in the numerical simulations. Finally, the discrete fractional memristor model is applied to the Logistic map, and we construct a new chaotic map called the discrete fracmemristor Logistic map. The new chaotic sequence is observed. In addition, it provides important mathematical models for many fields, such as chaotic systems, chaotic circuits, and neural networks.

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Acknowledgements

The author acknowledges the referees and the editor for carefully reading this paper and giving many helpful comments. This work is supported by the Natural Science Basic Research Program of Shaanxi (2021JM-533, 2021JQ-880, 2020JM-646, 2022JM-029), the Innovation Capability Support Program of Shaanxi (2018GHJD-21), the Science and Technology Program of Xi’an (2019218414GXRC020CG021-GXYD20.3), the Support Plan for Sanqin Scholars Innovation Team in Shaanxi Province of China, the Scientific Research Program Funded by Shaanxi Provincial Education Department (21JK0960), the Scientific Research Foundation of Xijing University (XJ21B01), and the Scientific Research Foundation of Xijing University (XJ200202). The authors also express their gratitude to the reviewers for their insightful comments.

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Authors and Affiliations

  1. Xi’an Key Laboratory of Advanced Photo-electronics Materials and Energy Conversion Device, School of Science, Xijing University, Xi’an, 710123, People’s Republic of China

    Xiaomin Li, Zhen Wang, Mingshu Chen & Yang Wang

  2. Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source, School of Science, Xijing University, Xi’an, 710123, People’s Republic of China

    Zhen Wang

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  1. Xiaomin Li
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  2. Zhen Wang
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  3. Mingshu Chen
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  4. Yang Wang
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Xiaomin Li: formation of overall research ideas, writing—original draft preparation. Zhen Wang: writing—reviewing and editing, submission and contact with editors. Mingshu Chen: typesetting. Yang Wang: programming.

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Correspondence to Zhen Wang.

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Li, X., Wang, Z., Chen, M. et al. Discrete fracmemristor model with the window function and its application in Logistic map. Eur. Phys. J. Spec. Top. 231, 3197–3207 (2022). https://doi.org/10.1140/epjs/s11734-022-00567-w

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