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Synchronization of chaotic-type delayed neural networks and its application

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Abstract

Our proposed image encryption is based on synchronization of chaotic fuzzy cellular neural networks (FCNNs) with different time delays and uses sampled-data controller. (i) It is known that the chaotic system plays a vital role in secure communication. (ii) FCNNs are more suitable for image processing due to its local connectedness. (iii) There are some results derived on theory part for the problem of synchronization of chaotic delayed FCNNs. (iv) We raise the following question: Is it possible to utilize these obtained chaotic values via FCNNs to image encryption? (v) Finally, we tried the above and succeed. Moreover, numerical instance and comparison results show that the proposed scheme works well and is resistant to differential attack.

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References

  1. Kaur, R., Singh, E.K.: Image encryption techniques: a selected review. J. Comput. Eng. (IOSR-JCE) 9, 80–83 (2013)

    Article  Google Scholar 

  2. Feng, G.: Principle and Network Security Technology. Science Press, Beijing (2003)

    Google Scholar 

  3. Yu, L., Wang, Z., Wang, W.: The application of hybrid encryption algorithm in software security. In: 4th IEEE International Conference on Computational Intelligence and Communication Networks, pp. 762-765 (2012)

  4. Enayatifar, R., Sadaei, H.J., Abdullah, A.H., Lee, M., Isnin, I.F.: A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt. Lasers Eng. 71, 33–41 (2015)

    Article  Google Scholar 

  5. Carroll, T.L., Pecora, L.M.: Synchronization chaotic circuits. IEEE Trans. Circuits Syst. 38, 453–456 (1991)

    Article  Google Scholar 

  6. Pecora, L.M., Carroll, T.L.: Synchronization in chaotic systems. Phys. Rev. Lett. 64, 821–824 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kwon, O.M., Park, J.H., Lee, S.M.: Secure communication based on chaotic synchronization via interval time-varying delay feedback control. Nonlinear Dyn. 63, 239–252 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  8. Moskalenko, O.I., Koronovskii, A.A., Hramov, A.E.: Generalized synchronization of chaos for secure communication: remarkable stability to noise. Phys. Lett. A 374, 2925–2931 (2010)

    Article  MATH  Google Scholar 

  9. Wang, H., Han, Z., Zhang, W., Xie, Q.: Chaotic synchronization and secure communication based on descriptor observer. Nonlinear Dyn. 57, 69–73 (2009)

    Article  MATH  Google Scholar 

  10. Niyat, A.Y., Moattar, M.H., Torshiz, M.N.: Color image encryption based on hybrid hyper-chaotic system and cellular automata. Opt. Lasers Eng. 90, 225–237 (2017)

    Article  Google Scholar 

  11. Wang, Z., Huang, L.: Synchronization analysis of linearly coupled delayed neural networks with discontinuous activations. Appl. Math. Model. 39, 7427–7441 (2015)

    Article  MathSciNet  Google Scholar 

  12. Assad, S.E., Farajallah, M.: A new chaos-based image encryption system. Signal Process. Image Commun. 41, 144–157 (2016)

    Article  Google Scholar 

  13. Zhao, J., Wang, S., Chang, Y., Li, X.: A novel image encryption scheme based on an improper fractional-order chaotic system. Nonlinear Dyn. 80, 1721–1729 (2015)

    Article  MathSciNet  Google Scholar 

  14. Xie, E.Y., Li, C., Yu, S., Lü, J.: On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process. 132, 150–154 (2017)

    Article  Google Scholar 

  15. Özkaynak, F.: Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn. 1–9 (2018)

  16. Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: theory. In: Proceedings of the IEEE International Workshop on Cellular Neural Networks and Applications, pp. 181–186 (1996)

  17. Yang, T., Yang, L.B., Wu, C.W., Chua, L.O.: Fuzzy cellular neural networks: applications. In: Proceedings of the IEEE International Workshop on Cellular Neural Networks and Applications, pp. 225–230 (1996)

  18. 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, 1493–1502 (2015)

    Article  MathSciNet  Google Scholar 

  19. Chen, L., Wu, R., Pan, D.: Mean square exponential stability of impulsive stochastic fuzzy cellular neural networks with distributed delays. Expert Syst. Appl. 38, 6294–6299 (2011)

    Article  Google Scholar 

  20. Liu, Z., Zhang, H., Wang, Z.: Novel stability criterions of a new fuzzy cellular neural networks with time-varying delays. Neurocomputing 72, 1056–1064 (2009)

    Article  Google Scholar 

  21. Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Stationary oscillation of interval fuzzy cellular neural networks with mixed delays under impulsive perturbations. Neural Comput. Appl. 22, 1645–1654 (2013)

    Article  Google Scholar 

  22. Li, X., Rakkiyappan, R., Balasubramaniam, P.: Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J. Frankl. Inst. 348, 135–155 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Global asymptotic stability of BAM fuzzy cellular neural networks with time delay in the leakage term, discrete and unbounded distributed delays. Math. Comput. Model. 53, 839–853 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  24. Balasubramaniam, P., Kalpana, M., Rakkiyappan, R.: Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst. Signal Process. 30, 1595–1616 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  25. Gopalsamy, K.: Stability and Oscillations in Delay Differential Equations of Population Dynamics. Mathematics and Its Applications, vol. 74. Springer, Dordrecht (1992)

    Book  MATH  Google Scholar 

  26. Gan, Q., Xu, R., Yang, P.: Synchronization of non-identical chaotic delayed fuzzy cellular neural networks based on sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 17, 433–443 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  27. Yu, J., Hu, C., Jiang, H., Teng, Z.: Exponential lag synchronization for delayed fuzzy cellular neural networks via periodically intermittent control. Math. Comput. Simul. 82, 895–908 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  28. Lu, J., Hill, D.J.: Global asymptotical synchronization of chaotic Lur’e systems using sampled data: a linear matrix inequality approach. IEEE Trans. Circuits Syst. II(55), 586–590 (2008)

    Google Scholar 

  29. Gan, Q., Liang, Y.: Synchronization of chaotic neural networks with time delay in the leakage term and parametric uncertainties based on sampled-data control. J. Frankl. Inst. 349, 1955–1971 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  30. Li, N., Zhang, Y., Hu, J., Nie, Z.: Synchronization for general complex dynamical networks with sampled-data. Neurocomputing 74, 805–811 (2011)

    Article  Google Scholar 

  31. Li, C., Lin, D., Lü, J.: Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE MultiMed. 24, 64–71 (2017)

    Article  Google Scholar 

  32. Li, C., Liu, Y., Xie, T., Chen, M.Z.Q.: Breaking a novel image encryption scheme based on improved hyperchaotic sequences. Nonlinear Dyn. 73, 2083–2089 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  33. Dang, P.P., Chau, P.M.: Image encryption for secure Internet multimedia applications. IEEE Trans. Consum. Electron. 46, 395–403 (2000)

    Article  Google Scholar 

  34. Fridman, E., Seuret, A., Richard, J.P.: Robust sampled-data stabilization of linear systems: an input delay approach. Automatica 40, 1441–1446 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  35. Boyd, S., Ghaoui, L.E., Feron, E., Balakrishnan, V.: Linear Matrix Inequalities in Systems and Control Theory. SIAM, Philadelphia (1994)

    Book  MATH  Google Scholar 

  36. Sanchez, E.N., Perez, J.P.: Input-to-state stability (ISS) analysis for dynamic neural networks. IEEE Trans. Circuits Syst. I(46), 1395–1398 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  37. Yang, T., Yang, L.B.: Global stability of fuzzy cellular neural network. IEEE Trans. Circuits Syst. I(43), 880–883 (1996)

    Article  MathSciNet  Google Scholar 

  38. Gu, K.: An integral inequality in the stability problem of time-delay systems. In: Proceedings of the 39th IEEE Conference on Decision and Control Sydney, Australia, pp. 2805-2810 (2000)

  39. Li, T., Fei, S., Zhu, Q.: Design of exponential state estimator for neural networks with distributed delays. Nonlinear Anal. Real World Appl. 10, 1229–1242 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  40. Boeing, G.: Visual analysis of nonlinear dynamical systems: chaos, fractals, self-similarity and the limits of prediction. Systems 4, 37–54 (2016)

    Article  Google Scholar 

  41. Liu, H., Kadir, A.: Asymmetric color image encryption scheme using 2D discrete-time map. Signal Process. 113, 104–112 (2015)

    Article  Google Scholar 

  42. Dong, C.: Color image encryption using one-time keys and coupled chaotic systems. Signal Process. Image Commun. 29, 628–640 (2014)

    Article  Google Scholar 

  43. Wei, X., Guo, L., Zhang, Q., Zhang, J., Lian, S.: A novel color image encryption algorithm based on DNA sequence operation and hyper-chaotic system. J. Syst. Softw. 85, 290–299 (2012)

    Article  Google Scholar 

  44. Wang, X., Zhao, Y., Zhang, H., Guo, K.: A novel color image encryption scheme using alternate chaotic mapping structure. Opt. Lasers Eng. 82, 79–86 (2016)

    Article  Google Scholar 

  45. Wang, X., Zhang, H.: A color image encryption with heterogeneous bit-permutation and correlated chaos. Opt. Commun. 342, 51–60 (2015)

    Article  Google Scholar 

  46. Wu, X., Kan, H., Kurths, J.: A new color image encryption scheme based on DNA sequences and multiple improved 1D chaotic maps. Appl. Soft Comput. 37, 24–39 (2015)

    Article  Google Scholar 

Download references

Acknowledgements

This effort was assisted by the Fundamental Research Grant Scheme (FRGS) from MoHE under Grant No. FP051-2016. Dr. M. Kalpana is working as a Post-doctoral Research Fellow at the University of Malaya.

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Authors and Affiliations

  1. Institute of Mathematical Sciences, Faculty of Science, University of Malaya, 50603, Kuala Lumpur, Malaysia

    M. Kalpana & K. Ratnavelu

  2. Department of Mathematics, Gandhigram Rural Institute - Deemed University, Gandhigram, Tamilnadu, 624 302, India

    P. Balasubramaniam

  3. Centre for Foundation Studies in Science, University of Malaya, 50603, Kuala Lumpur, Malaysia

    M. Z. M. Kamali

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  1. M. Kalpana
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  2. K. Ratnavelu
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  3. P. Balasubramaniam
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  4. M. Z. M. Kamali
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Correspondence to K. Ratnavelu.

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Kalpana, M., Ratnavelu, K., Balasubramaniam, P. et al. Synchronization of chaotic-type delayed neural networks and its application. Nonlinear Dyn 93, 543–555 (2018). https://doi.org/10.1007/s11071-018-4208-z

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  • DOI: https://doi.org/10.1007/s11071-018-4208-z

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