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Hopfield neural network with multi-scroll attractors and application in image encryption

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Abstract

Hopfield neural networks are favored by academia and industrial fields due to their abundant dynamics. In this paper, the dynamical behavior of a small Hopfield neural network (HNN) simultaneously stimulated by electromagnetic radiation and multi-level-logic pulse is investigated. Firstly, a modified HNN with three neurons is presented by selecting appropriate synapse weight coefficients. And the system model of the HNN under electromagnetic radiation and an electrical pulse is constructed. Then its equilibrium stabilities and nonlinear dynamical phenomena are analyzed by using numerical analysis methods including phase portraits, Lyapunov exponents, and bifurcation diagrams. The research results show that the neural network affected by electromagnetic radiation and a multi-level-logic pulse signal can generate chaotic multi-scroll attractors, which has not been observed in the previous investigation for the Hopfield-type neural networks. In addition, the number of the scroll can be easily changed by adjusting the electrical pulse signal. Circuit simulations based on the designed neural network circuit are carried out to confirm the numerical simulations. Finally, an HNN-based image encryption scheme is designed from the perspective of engineering applications. Performance evaluations demonstrate that the proposed image cryptosystem has good security.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (62271197,61971185), the Natural Science Foundation of Hunan Province (2020JJ4218). All authors certify that they have no affiliations with or involvement in any organization or entity with any financial interest or non-financial interest in the subject matter or materials discussed in this manuscript.

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  1. College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082, China

    Zhenhua Hu & Chunhua Wang

  2. College of Science, Hunan City University, Yiyang, 413000, China

    Zhenhua Hu

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  1. Zhenhua Hu
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Correspondence to Chunhua Wang.

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Hu, Z., Wang, C. Hopfield neural network with multi-scroll attractors and application in image encryption. Multimed Tools Appl 83, 97–117 (2024). https://doi.org/10.1007/s11042-023-15670-w

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