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Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network

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Abstract

Memristors are widely considered to be promising candidates to mimic biological synapses. In this paper, by introducing a non-ideal flux-controlled memristor model into a Hopfield neural network (HNN), a novel memristive HNN model with multi-double-scroll attractors is constructed. The parity of the number of double scrolls can be flexibly controlled by the internal parameters of the memristor. Through theoretical analysis and numerical simulation, various coexisting attractors and amplitude control are observed. Particularly, the interesting and rare phenomenon of the memristor initial offset boosting coexisting dynamics is discovered, in which the initial offset boosting coexisting double-scroll attractors with banded attraction basins are distributed in a line along the boosting route with the variation of the memristor initial condition. In addition, it is also found that the number of the initial offset boosting coexisting double-scroll attractors is closely related to the total number of scrolls and ultimately tends to infinity with increasing the total number of scrolls, meaning the emergence of extreme multistability. Then, the random performance of the initial offset boosting coexisting double-scroll attractors is tested by the NIST test suite. Moreover, an encryption scheme based on them is also proposed. The obtained results show that they have excellent randomness and are suitable for image encryption application. Finally, numerical simulation results are well demonstrated by circuit experiments, showing the feasibility of the designed memristive multi-double-scroll HNN model.

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Acknowledgements

The authors would like to thank the Editor-in-Chief, the Associate Editor and the anonymous reviewers for their insightful suggestions and constructive comments. This work was supported by the grants from the National Natural Science Foundation of China under 61876209 and the National Key Research and Development Program of China under 2017YFC1501301.

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Authors and Affiliations

  1. Institute of Artificial Intelligence, School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, 430074, China

    Sen Zhang

  2. School of Artificial Intelligence and Automation and the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Huazhong University of Science and Technology, Wuhan, 430074, China

    Jiahao Zheng, Xiaoping Wang & Zhigang Zeng

  3. School of Physics and Electronics, Central South University, Changsha, 410083, Hunan, China

    Shaobo He

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  1. Sen Zhang
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  2. Jiahao Zheng
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  3. Xiaoping Wang
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  4. Zhigang Zeng
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Correspondence to Xiaoping Wang.

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Zhang, S., Zheng, J., Wang, X. et al. Initial offset boosting coexisting attractors in memristive multi-double-scroll Hopfield neural network . Nonlinear Dyn 102, 2821–2841 (2020). https://doi.org/10.1007/s11071-020-06072-w

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