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Fixed-time Synchronization of Complex-valued Memristive BAM Neural Network and Applications in Image Encryption and Decryption

  • Yongzhen Guo
  • Yang LuoEmail author
  • Weiping Wang
  • Xiong Luo
  • Chao Ge
  • Jürgen Kurths
  • Manman Yuan
  • Yang Gao
Article
  • 9 Downloads

Abstract

This paper focuses on the dynamical characteristics of complex-valued memristor-based BAM neural network (CVMBAMNN) with leakage time-varying delay. With two different controllers, we have obtained fixedtime and finite-time synchronization criteria respectively in complex domain for our special model, which few work has studied before. Since fixed-time synchronous system can improve communication security, we designed a scheme for RGB image encryption and decryption. In order to satisfy the requirement of much lower error in image secure communication, our approach can get the error of fixed-time synchronization to about 1×1013. Due to our highly consistent system, we do get good encryption and decryption effect with encryption and decryption scheme. Finally, numerical simulations are included to demonstrate the correctness of our theoretical results.

Keywords

Chaotic character complex-valued MBAMNN fixed-time synchronization image encryption and decryption leakage time-varying delay 

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References

  1. [1]
    B. Kosko, “Bidirectional associative memories,” Systems Man & Cybernetics IEEE Transactions on, vol. 18, no. 1, pp. 49–60, 1988.MathSciNetCrossRefGoogle Scholar
  2. [2]
    B. Fa, Y. Yin, and C. Fu, “The bidirectional associative memory neural network based on fault tree and its application to inverter’s fault diagnosis,” Proc. of IEEE International Conference on Intelligent Computing and Intelligent Systems, ICIS 2009., vol. 1, pp. 209–213, 2009.Google Scholar
  3. [3]
    G. Mathai and B. R. Upadhyaya, “Performance analysis and application of the bidirectional associative memory to industrial spectral signatures,” International Joint Conference on Neural Networks, IEEE, vol. 1, pp. 33–37, 1989.CrossRefGoogle Scholar
  4. [4]
    W. P. Wang, M. H. Yu, X. Luo, L. L. Liu, M. M. Yuan, and W. B. Zhao, “Synchronization of memristive BAM neural networks with leakage delay and additive time-varying delay components via sampled-data control,” Chaos, Solitons & Fractals, vol. 104, pp. 84–97, 2017.MathSciNetCrossRefGoogle Scholar
  5. [5]
    D. Liu, S. Zhu, and E. Ye, “Synchronization stability of memristor-based complex-valued neural networks with time delays,” Neural Networks, vol. 96, pp. 115–127, 2017.CrossRefGoogle Scholar
  6. [6]
    J. M. Zurada, I. Aizenberg, and M. A. Mazurowski, “Learning in networks: complex-valued neurons, pruning, and rule extraction,” Proc. of the 4th International IEEE Conference on Intelligent Systems, IS’08, vol. 1, pp. 1–15-1-20, 2008.Google Scholar
  7. [7]
    J. Rubio, “Stable Kalman filter and neural network for the chaotic systems identification,” Journal of the Franklin Institute, vol. 354, no. 16, pp. 7444–7462, 2017.MathSciNetCrossRefGoogle Scholar
  8. [8]
    E. Lughofer, S. Kindermann, M. Pratama, and J. Rubio, “Top-down sparse fuzzy regression modeling from data with improved coverage,” International Journal of Fuzzy Systems, vol. 19, no. 5, pp. 1645–1658, 2017.MathSciNetCrossRefGoogle Scholar
  9. [9]
    J. Rubio, E. Lughofer, J. A. Meda-Campaña, L. A. Páramo, J. F. Novoa, and J. Pacheco, “Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models,” Journal of Intelligent, Fuzzy Systems, vol. 35, no. 2, pp. 2585–2596, 2018.CrossRefGoogle Scholar
  10. [10]
    J. Rubio, E. Lughofer, A. Plamen, J. F. Novoa, and J. A. Meda-Campaña, “A novel algorithm for the modeling of complex processes,” Kybernetika, vol. 54, no. 1, pp. 79–95, 2018.MathSciNetzbMATHGoogle Scholar
  11. [11]
    M. Kar, M. K. Mandal, and D. Nandi, “RGB image encryption using hyper chaotic system,” Research in Computational Intelligence and Communication Networks (ICRCICN), 2017 Third International Conference on. IEEE, pp. 354–359, 2017.Google Scholar
  12. [12]
    H. Liu, Z. Wang, B. Shen, and X. Liu, “Event-triggered H∞ state estimation for delayed stochastic memristive neural networks with missing measurements: the discrete time case,” IEEE Transactions on Neural Networks and Learning Systems, vol. 29, no. 8, pp. 3726–3737, 2017.MathSciNetGoogle Scholar
  13. [13]
    X. Li, X. Fu, P. Balasubramaniam, and R. Rakkiyappan, “Existence, uniqueness and stability analysis of recurrent neural networks with time delay in the leakage term under impulsive perturbations,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 4092–4108, 2010.MathSciNetCrossRefGoogle Scholar
  14. [14]
    Z. S. Wang, J. Sun, and H. G. Zhang, “Stability analysis of T-S fuzzy control system with sampled-dropouts based on time-varying Lyapunov function method,” IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access), pp. 1–12, 2018.Google Scholar
  15. [15]
    G. Velmurugan, R. Rakkiyappan, and J. Cao, “Finite-time synchronization of fractional-order memristor-based neural networks with time delays,” Neural Networks the Official Journal of the International Neural Network Society, vol. 73, no. 1–2, pp. 36–46, 2015.zbMATHGoogle Scholar
  16. [16]
    J. Mei, M. H. Jiang, W. M. Xu, and B. Wang, “Finite-time synchronization control of complex dynamical networks with time delay,” Communications in Nonlinear Science & Numerical Simulation, vol. 18, no. 9, pp. 2462–2478, 2013.MathSciNetCrossRefGoogle Scholar
  17. [17]
    X. Yang, J. Lam, and D. W. C. Ho, “Fixed-time synchronization of complex networks with impulsive effects via nonchattering control,” IEEE Transactions on Automatic Control, vol. 62, no. 11, pp. 5511–5521, 2017.MathSciNetCrossRefGoogle Scholar
  18. [18]
    Y. Wan, J. Cao, G. Wen, and W. Yu, “Robust fixed-time synchronization of delayed Cohen-Grossberg neural networks,” Neural Networks, vol. 73, pp. 86–94, 2016.CrossRefGoogle Scholar
  19. [19]
    A. Polyakov, “Nonlinear feedback design for fixed-time stabilization of linear control systems,” IEEE Transactions on Automatic Control, vol. 57, no. 8, pp. 2106–2110, 2012.MathSciNetCrossRefGoogle Scholar
  20. [20]
    L. Sui, K. Duan, J. Liang, and X. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Optics Express, vol. 22, no. 9, pp. 10605–10621, 2014.CrossRefGoogle Scholar
  21. [21]
    S. Liu and F. Zhang, “Complex function projective synchronization of complex chaotic system and its applications in secure communication,” Nonlinear Dynamics, vol. 76, no. 2, pp. 1087–1097, 2014.MathSciNetCrossRefGoogle Scholar
  22. [22]
    R. Matthews, “On the derivation of a “chaotic” encryption algorithm,” Cryptologia, vol. 8, no. 8, pp. 29–41, 1989.MathSciNetCrossRefGoogle Scholar
  23. [23]
    C. Fu, Y. Zheng, M. Chen, and Z. K. Wen, “A color image encryption algorithm using a new 1-D chaotic map,” Proc. of IEEE 17th International Conference on Communication Technology (ICCT), IEEE, pp. 1768–1773, 2018.Google Scholar
  24. [24]
    H. C. Li, T. P. Zhang, and Z. M. Guo, “Adaptive control for a class of uncertain chaotic systems with saturation nonlinear input,” Proc. of the 9th International Conference on Electronic Measurement, Instruments, pp. 3–583-3-587, 2009.Google Scholar
  25. [25]
    J. Chen, J. Ping, and Z. Zeng, “Global Mittag-Leffler stability and synchronization of memristor-based fractionalorder neural networks,” Neural Networks, vol. 51, no. 3, pp. 1–8, 2014.CrossRefGoogle Scholar
  26. [26]
    G. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge Univ Press, Cambridge, 1952.zbMATHGoogle Scholar
  27. [27]
    X. Liu, W. Lu, and T. Chen, “Finite-time and fixed-time stability and synchronization,” Proc. of Control Conference IEEE, pp. 7985–7989, 2016.Google Scholar
  28. [28]
    J. H. Wang, W. S. Luo, and L. G. Wu, “Adaptive type-2 FNN-based dynamic sliding mode control of DC-DC boost converters,” IEEE Transactions on Systems, Man, and Cybernetics: Systems (Early Access), pp. 1–12, 2019.Google Scholar
  29. [29]
    M. Kar, M. K. Mandal, and D. Nandi, “RGB image encryption using hyper chaotic system,” Proc. of the 3rd International Conference on Research in Computational Intelligence and Communication Networks (ICRCICN), pp. 354–359, 2017.Google Scholar
  30. [30]
    A. Kadira, A. Hamdullaa, and W. Q. Guo, “Color image encryption using skew tent map and hyper chaotic system of 6th-order CNN,” Optik, vol. 125 pp. 1671–1675, 2014.Google Scholar
  31. [31]
    L. Zhang, X. Liao, and X. Wang, “An image encryption approach based on chaotic maps,” Chaos, Solitons & Fractals, vol. 24, pp. 759–765, 2005.MathSciNetCrossRefGoogle Scholar
  32. [32]
    S. Mazloom and A. M. Eftekhari-Moghadam, “Colour image encryption based on coupled nonlinear chaotic map,” Chaos, Solitons & Fractals, vol. 42, pp. 1745–1754, 2009.CrossRefGoogle Scholar
  33. [33]
    X. P. Wei, L. Guo, Q. Zhang, J. Zhang, and S. Lian, “A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system,” J. Syst. Software, vol. 85, pp. 290–299, 2012.CrossRefGoogle Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  • Yongzhen Guo
    • 1
    • 2
  • Yang Luo
    • 3
    Email author
  • Weiping Wang
    • 4
    • 5
    • 6
  • Xiong Luo
    • 7
  • Chao Ge
    • 8
  • Jürgen Kurths
    • 9
    • 10
  • Manman Yuan
    • 4
    • 5
    • 6
  • Yang Gao
    • 11
  1. 1.Beijing Institute of TechnologyBeijingChina
  2. 2.Software Testing CenterBeijingChina
  3. 3.School of Automation and Electrical EngineeringUniversity of Science and Technology Beijing (USTB)BeijingChina
  4. 4.School of Computer and Communication EngineeringUniversity of Science and Technology Beijing (USTB)BeijingChina
  5. 5.Beijing Key Laboratory of Knowledge Engineering for Materials ScienceBeijingChina
  6. 6.Institute of PhysicsHumboldt-UniversityBerlinGermany
  7. 7.School of Computer and Communication EngineeringUniversity of Science and Technology Beijing (USTB)BeijingChina
  8. 8.Chao Ge is with the Institute of Information EngineeringNorth China University of Science and TechnologyTangshanChina
  9. 9.Institute of PhysicsHumboldt-University BerlinBerlinGermany
  10. 10.Potsdam Institute for Climate Impact ResearchPotsdamGermany
  11. 11.China Information Technology Security Evaluation CenterBeijingChina

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