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Non-homogeneous Non-inductive Chaotic Circuit Based on Fractional-Order Active Generalized Memristor and its FPGA Implementation

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Abstract

In this paper, a novel active generalized fractional-order memristor is constructed by using a memristor diode bridge in parallel with a negative resistance. Combined with fractional calculus theory, the fractional-order model of the memristor is constructed by using predictive correction method. The model is connected in parallel with a capacitor to form a second-order nonlinear filter and coupled with an RC bridge oscillator to form a chaotic circuit. The fractional-order memristor model and the chaotic circuit it forms are novel. The mathematical model of the fractional-order memristor chaotic system is established, and its dynamic behavior is analyzed by theoretical calculation and numerical simulation. Dynamic characteristics of the system are verified by time series, phase diagram, bifurcation diagram and Lyapunov exponent spectrum, and the results of numerical simulation and analog outputs of electronic circuit are the same as expected. Finally, the fractional-order memristor chaotic circuit is realized by FPGA hardware circuit experiment, and its phase diagram is observed by oscilloscope to be consistent with numerical simulation and circuit simulation, which verifies the effectiveness of theoretical analysis.

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Data Availability

All data generated or analyzed during this study are included in this article [and its supplementary information files].

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Acknowledgements

Funding was provided by National Natural Science Foundation of China Grant No. (51507134) and Natural Science Foundation of Shaanxi Province Grant No. (2021JM-449, 2018JM5068).

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Authors and Affiliations

  1. School of Electrical Engineering, Xi’an University of Technology, Xi’an, 710048, Shaanxi, People’s Republic of China

    Ningning Yang & Ni Liu

  2. School of Electronics and Information, Xi’an Polytechnic University, Xi’an, 710048, Shaanxi, People’s Republic of China

    Chaojun Wu

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  1. Ningning Yang
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  2. Ni Liu
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Correspondence to Ningning Yang.

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Yang, N., Liu, N. & Wu, C. Non-homogeneous Non-inductive Chaotic Circuit Based on Fractional-Order Active Generalized Memristor and its FPGA Implementation. Circuits Syst Signal Process 42, 1940–1958 (2023). https://doi.org/10.1007/s00034-022-02213-1

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