Skip to main content
Log in

Dynamics analysis and image encryption application of Hopfield neural network with a novel multistable and highly tunable memristor

  • Original Paper
  • Published:
Nonlinear Dynamics Aims and scope Submit manuscript

Abstract

Building artificial neural network models and studying their dynamic behaviors is extremely important from both a theoretical and practical standpoint due to the rapid advancement of artificial intelligence . In addition to its engineering applications, this article concentrates primarily on the memristor model and chaotic dynamics of the asymmetric memristive neural network. First, we develop a novel memristor model, which is multistable and highly tunable. Using this memristor model to build an asymmetric memristive Hopfield neural network (AMHNN), the chaotic dynamics of the proposed AMHNN are investigated and analyzed using fundamental dynamics techniques such as equilibrium stability, bifurcation diagrams, and Lyapunov exponents. According to the findings of this study, the proposed AMHNN possesses a number of complex dynamic properties, including scaling amplitude chaos with coupling strength control, and coexisting uncommon chaotic attractors with initial control and coupling strength control. Significantly, the proposed AMHNN has been observed to exhibit the phenomenon of infinitely persisting uncommon chaotic attractors. In the interim, a system for image encryption based on the proposed AMHNN is constructed. By analyzing correlation, information entropy, and key sensitivity, the devised encryption method reveals a number of benefits. The feasibility of the encryption method is validated through field-programmable gate arrays hardware experiments, and the proposed memristor and AMHNN models have been translated into a Simulink model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17

Similar content being viewed by others

Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

References

  1. Chua, L.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18(5), 507–519 (1971)

    Google Scholar 

  2. Strukov, D.B., Snider, G.S., Stewart, D.R., Williams, R.S.: The missing memristor found. Nature 453(7191), 80–83 (2008)

    Google Scholar 

  3. Chua, L.: Device modeling via nonlinear circuit elements. IEEE Trans. Circuits Syst. 27(11), 1014–1044 (1980)

    MathSciNet  Google Scholar 

  4. Zhong, H., Li, G., Xu, X.: A generic voltage-controlled discrete memristor model and its application in chaotic map. Chaos, Solitons & Fractals 161, 112389 (2022)

    MathSciNet  Google Scholar 

  5. Peng, Y., Sun, K., He, S.: A discrete memristor model and its application in hénon map. Chaos, Solitons & Fractals 137, 109873 (2020)

    MathSciNet  Google Scholar 

  6. Lin, H., Wang, C., Hong, Q., Sun, Y.: A multi-stable memristor and its application in a neural network. IEEE Trans. Circuits Syst. II Express Briefs 67(12), 3472–3476 (2020)

    Google Scholar 

  7. Xie, W., Wang, C., Lin, H.: A fractional-order multistable locally active memristor and its chaotic system with transient transition, state jump. Nonlinear Dyn. 104(4), 4523–4541 (2021)

    Google Scholar 

  8. Wang, J., Zou, Y., Lei, P., Sherratt, R.S., Wang, L.: Research on recurrent neural network based crack opening prediction of concrete dam. J. Internet Technol. 21(4), 1161–1169 (2020)

    Google Scholar 

  9. Yu, F., Liu, L., Xiao, L., Li, K., Cai, S.: A robust and fixed-time zeroing neural dynamics for computing time-variant nonlinear equation using a novel nonlinear activation function. Neurocomputing 350, 108–116 (2019)

    Google Scholar 

  10. Yao, W., Yu, F., Zhang, J., Zhou, L.: Asymptotic synchronization of memristive cohen-grossberg neural networks with time-varying delays via event-triggered control scheme. Micromachines 13(5), 726 (2022)

    Google Scholar 

  11. Wang, J., Wu, Y., He, S., Sharma, P.K., Yu, X., Alfarraj, O., Tolba, A.: Lightweight single image super-resolution convolution neural network in portable device. KSII Trans. Internet & Inf. Syst.15(11) (2021)

  12. Long, M., Zeng, Y.: Detecting iris liveness with batch normalized convolutional neural network. Comput., Mater. & Continua 58(2), 493–504 (2019)

    Google Scholar 

  13. Yao, W., Wang, C., Sun, Y., Zhou, C.: Robust multimode function synchronization of memristive neural networks with parameter perturbations and time-varying delays. IEEE Trans. Syst., Man, Cybernetics: Syst. 52(1), 260–274 (2020)

    Google Scholar 

  14. Lin, H., Wang, C., Deng, Q., Xu, C., Deng, Z., Zhou, C.: Review on chaotic dynamics of memristive neuron and neural network. Nonlinear Dyn. 106(1), 959–973 (2021)

    Google Scholar 

  15. Yao, Z., Sun, K., He, S.: Firing patterns in a fractional-order fithzhugh-nagumo neuron model. Nonlinear Dyn. 110(2), 1807–1822 (2022)

    Google Scholar 

  16. Yao, W., Wang, C., Sun, Y., Zhou, C., Lin, H.: Exponential multistability of memristive cohen-grossberg neural networks with stochastic parameter perturbations. Appl. Math. Comput. 386, 125483 (2020)

    MathSciNet  Google Scholar 

  17. Xu, L., Qi, G., Ma, J.: Modeling of memristor-based hindmarsh-rose neuron and its dynamical analyses using energy method. Appl. Math. Model. 101, 503–516 (2022)

    MathSciNet  Google Scholar 

  18. Lin, H., Wang, C., Cui, L., Sun, Y., Xu, C., Yu, F.: Brain-like initial-boosted hyperchaos and application in biomedical image encryption. IEEE Trans. Industr. Inf. 18(12), 8839–8850 (2022)

    Google Scholar 

  19. Qiu, H., Xu, X., Jiang, Z., Sun, K., Cao, C.: Dynamical behaviors, circuit design, and synchronization of a novel symmetric chaotic system with coexisting attractors. Sci. Rep. 13(1), 1893 (2023)

    Google Scholar 

  20. Doubla, I.S., Ramakrishnan, B., Njitacke, Z.T., Kengne, J., Rajagopal, K.: Hidden extreme multistability and its control with selection of a desired attractor in a non-autonomous hopfield neuron. AEU-Int. J. Electr. Commun. 144, 154059 (2022)

    Google Scholar 

  21. Chen, C., Chen, J., Bao, H., Chen, M., Bao, B.: Coexisting multi-stable patterns in memristor synapse-coupled hopfield neural network with two neurons. Nonlinear Dyn. 95, 3385–3399 (2019)

    Google Scholar 

  22. Zhang, S., Zheng, J., Wang, X., Zeng, Z., He, S.: Initial offset boosting coexisting attractors in memristive multi-double-scroll hopfield neural network. Nonlinear Dyn. 102, 2821–2841 (2020)

    Google Scholar 

  23. Lin, H., Wang, C., Sun, J., Zhang, X., Sun, Y., Iu, H.H.: Memristor-coupled asymmetric neural networks: bionic modeling, chaotic dynamics analysis and encryption application. Chaos, Solitons & Fractals 166, 112905 (2023)

    MathSciNet  Google Scholar 

  24. Fahimi, Z., Mahmoodi, M., Nili, H., Polishchuk, V., Strukov, D.: Combinatorial optimization by weight annealing in memristive hopfield networks. Sci. Rep. 11(1), 16383 (2021)

    Google Scholar 

  25. Long, M., Peng, F., Li, H.: Separable reversible data hiding and encryption for hevc video. J. Real-Time Image Proc. 14, 171–182 (2018)

    Google Scholar 

  26. Lai, Q., Lai, C., Zhang, H., Li, C.: Hidden coexisting hyperchaos of new memristive neuron model and its application in image encryption. Chaos, Solitons & Fractals 158, 112017 (2022)

    MathSciNet  Google Scholar 

  27. Zhou, S., Wang, X., Zhang, Y., Ge, B., Wang, M., Gao, S.: A novel image encryption cryptosystem based on true random numbers and chaotic systems. Multimedia Syst. 28, 95–112 (2022)

    Google Scholar 

  28. Chen, Y., Xie, S., Zhang, J.: A hybrid domain image encryption algorithm based on improved henon map. Entropy 24(2), 287 (2022)

    MathSciNet  Google Scholar 

  29. Zhou, S., Qiu, Y., Wang, X., Zhang, Y.: Novel image cryptosystem based on new 2d hyperchaotic map and dynamical chaotic s-box. Nonlinear Dyn. 111(10), 9571–9589 (2023)

    Google Scholar 

  30. Bigdeli, N., Farid, Y., Afshar, K.: A robust hybrid method for image encryption based on hopfield neural network. Comput. & Electr. Eng. 38(2), 356–369 (2012)

    Google Scholar 

  31. Lai, Q., Wan, Z., Zhang, H., Chen, G.: Design and analysis of multiscroll memristive hopfield neural network with adjustable memductance and application to image encryption. IEEE Transactions on Neural Networks and Learning Systems pp. 1–14 (2022)

  32. Yu, F., Shen, H., Yu, Q., Kong, X., Sharma, P.K., Cai, S.: Privacy protection of medical data based on multi-scroll memristive hopfield neural network. IEEE Transactions on Network Science and Engineering p. 726 (2022)

  33. Wang, S., Cao, Y., Wen, S., Guo, Z., Huang, T., Chen, Y.: Projective synchroniztion of neural networks via continuous periodic event-based sampling algorithms. IEEE Trans. Netw. Sci. Eng. 7(4), 2746–2754 (2020)

    MathSciNet  Google Scholar 

  34. Yao, W., Wang, C., Sun, Y., Gong, S., Lin, H.: Event-triggered control for robust exponential synchronization of inertial memristive neural networks under parameter disturbance. Neural Netw. 164, 67–80 (2023)

    Google Scholar 

  35. Breakspear, M.: Dynamic models of large-scale brain activity. Nat. Neurosci. 20(3), 340–352 (2017)

    Google Scholar 

  36. Sah, M.P., Yang, C., Kim, H., Muthuswamy, B., Jevtic, J., Chua, L.: A generic model of memristors with parasitic components. IEEE Trans. Circuits Syst. I Regul. Pap. 62(3), 891–898 (2015)

    MathSciNet  Google Scholar 

  37. Chua, L.: If it’s pinched it’s a memristor. Semicond. Sci. Technol. 29(10), 104001 (2014)

    Google Scholar 

  38. Chua, L.: Everything you wish to know about memristors but are afraid to ask. Radioengineering 24, 319–368 (2015)

    Google Scholar 

  39. Jiang, Y., Li, C., Zhang, C., Zhao, Y., Zang, H.: A double-memristor hyperchaotic oscillator with complete amplitude control. IEEE Trans. Circuits Syst. I Regul. Pap. 68(12), 4935–4944 (2021)

    Google Scholar 

  40. Bao, H., Hua, Z., Li, H., Chen, M., Bao, B.: Memristor-based hyperchaotic maps and application in auxiliary classifier generative adversarial nets. IEEE Trans. Industr. Inf. 18(8), 5297–5306 (2022)

    Google Scholar 

  41. Ping, J., Zhu, S., Shi, M., Wu, S., Shen, M., Liu, X., Wen, S.: Event-triggered finite-time synchronization control for quaternion-valued memristive neural networks by an non-decomposition method. IEEE Transactions on Network Science and Engineering pp. 1–10 (2023)

  42. Ye, X., Wang, X.: Hidden oscillation and chaotic sea in a novel 3d chaotic system with exponential function. Nonlinear Dyn. 111, 15477–15486 (2023)

    Google Scholar 

  43. Wen, S., Zeng, Z., Huang, T., Meng, Q., Yao, W.: Lag synchronization of switched neural networks via neural activation function and applications in image encryption. IEEE Trans. Neural Netw. Learn. Syst. 26(7), 1493–1502 (2015)

    MathSciNet  Google Scholar 

  44. Liu, L., Zhang, L., Jiang, D., Guan, Y., Zhang, Z.: A simultaneous scrambling and diffusion color image encryption algorithm based on hopfield chaotic neural network. IEEE Access 7, 185796–185810 (2019)

    Google Scholar 

  45. Zhou, S., Wang, X., Zhang, Y.: Novel image encryption scheme based on chaotic signals with finite-precision error. Inf. Sci. 621, 782–798 (2023)

    Google Scholar 

  46. Xia, Z., Wang, L., Tang, J., Xiong, N.N., Weng, J.: A privacy-preserving image retrieval scheme using secure local binary pattern in cloud computing. IEEE Trans. Netw. Sci. Eng. 8(1), 318–330 (2021)

    MathSciNet  Google Scholar 

  47. Benkouider, K., Vaidyanathan, S., Sambas, A., Tlelo-Cuautle, E., Abd El-Latif, A.A., Abd-El-Atty, B., Bermudez-Marquez, C.F., Sulaiman, I.M., Awwal, A.M., Kumam, P.: A new 5-d multistable hyperchaotic system with three positive lyapunov exponents: Bifurcation analysis, circuit design, fpga realization and image encryption. IEEE Access 10, 90111–90132 (2022)

    Google Scholar 

  48. Yao, W., Gao, K., Zhang, Z., Cui, L., Zhang, J.: An image encryption algorithm based on a 3d chaotic hopfield neural network and random row-column permutation. Front. Phys. 11, 1162887 (2023)

    Google Scholar 

  49. Jithin, K., Sankar, S.: Colour image encryption algorithm combining arnold map, dna sequence operation, and a mandelbrot set. J. Inf. Security Appl. 50, 102428 (2020)

    Google Scholar 

  50. Wu, Y., Noonan, J.P., Agaian, S., et al.: Npcr and uaci randomness tests for image encryption Cyber journals: multidisciplinary journals in science and technology. J. Selected Areas Telecommun. (JSAT) 1(2), 31–38 (2011)

    Google Scholar 

  51. Ye, X., Wang, X., Gao, S., Mou, J., Wang, Z., Yang, F.: A new chaotic circuit with multiple memristors and its application in image encryption. Nonlinear Dyn. 99, 1489–1506 (2020)

    Google Scholar 

  52. Xu, C., Sun, J., Wang, C.: An image encryption algorithm based on random walk and hyperchaotic systems. Int. J. Bifurcation and Chaos 30(04), 2050060 (2020)

  53. Lai, Q., Wan, Z., Zhang, H., Chen, G.: Design and analysis of multiscroll memristive hopfield neural network with adjustable memductance and application to image encryption. IEEE Transactions on Neural Networks and Learning Systems pp. 1–14 (2022)

  54. Wang, T., Song, L., Wang, M., Zhuang, Z.: A novel image encryption algorithm based on parameter-control scroll chaotic attractors. IEEE Access 8, 36281–36292 (2020)

    Google Scholar 

  55. Lin, H., Wang, C., Yu, F., Xu, C., Hong, Q., Yao, W., Sun, Y.: An extremely simple multiwing chaotic system: dynamics analysis, encryption application, and hardware implementation. IEEE Trans. Industr. Electron. 68(12), 12708–12719 (2020)

    Google Scholar 

  56. Sambas, A., Vaidyanathan, S., Tlelo-Cuautle, E., Abd-El-Atty, B., et al.: A 3-d multi-stable system with a peanut-shaped equilibrium curve: circuit design, fpga realization, and an application to image encryption. IEEE Access 8, 137116–137132 (2020)

    Google Scholar 

  57. Slavova, A., Tetzlaff, R.: Edge of chaos in memristor cnn with hysteresis and applications in pattern formation. 2021 IEEE International Symposium on Circuits and Systems (ISCAS) pp. 1–4 (2021)

  58. Kong, X., Yu, F., Yao, W., Xu, C., Zhang, J., Cai, S., Wang, C.: A class of 2n+1 dimensional simplest hamiltonian conservative chaotic systems and fast image encryption schemes. Appl. Math. Model. (2023). https://doi.org/10.1016/j.apm.2023.10.004

    Article  Google Scholar 

Download references

Acknowledgements

This work was partially supported by the National Natural Science Foundation of China (62201204), the Hunan Provincial Natural Science Foundation of China (2022JJ40514, 2022JJ30624), the Scientific Research Foundation of Hunan Provincial Education Department, China (21B0345, 21C0200), the Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province, Changsha University of Science and Technology, China (kfj220603), and the Open Research Project of the State Key Laboratory of Industrial Control Technology, Zhejiang University, China (No. ICT2023B38).

Author information

Authors and Affiliations

Authors

Contributions

All authors read and approved the final manuscript.

Corresponding author

Correspondence to Wei Yao.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, W., Liu, J., Sun, Y. et al. Dynamics analysis and image encryption application of Hopfield neural network with a novel multistable and highly tunable memristor. Nonlinear Dyn 112, 693–708 (2024). https://doi.org/10.1007/s11071-023-09041-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11071-023-09041-1

Keywords

Navigation