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Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit

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Abstract

A novel memristive chaotic circuit is proposed by replacing the Chua’s diode in modified Chua’s circuit with a smooth active memristor, and the corresponding memristive model is analyzed and validated. The equilibrium point set, dissipativity and stability of this new chaotic circuit are developed theoretically. The dynamic characteristics for the new system are presented by means of phase diagrams, Lyapunov exponents, bifurcation diagrams and Poincaré maps. The coexistence of the memristive system is carried out from the perspective of asymmetric coexistence and symmetry coexistence. In addition, the coexistence of multiple states is studied by a more direct method with initial value as the system variable to gain a more intuitive observation. The circuit model of the memristive chaotic system is designed through Multisim simulation software. Finally, the memristive chaotic sequence is used to encrypt the image, and the influence of multistability on the encryption is investigated by the histogram, correlation and key sensitivity. The results show that the proposed new memristive chaotic system has high security.

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References

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

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Yang, J.J., Strukov, D.B., Stewart, D.R.D.: Memristive devices for computing. Nat. Nanotechnol. 8, 13–24 (2012)

    Article  Google Scholar 

  4. Wang, W.P., Li, L.X., Peng, H.P.: Anti-synchronization of coupled memristive neutral-type neural networks with mixed time-varying delays via randomly occurring control. Nonlinear Dyn. 83, 2143–2155 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bao, H.B., Park, J.H., Cao, J.D.: Adaptive synchronization of fractional-order memristor-based neural networks with time delay. Nonlinear Dyn. 82, 1–12 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Hu, X., Feng, G., Duan, S., Liu, L.: A memristive multilayer cellular neural network with applications to image processing. IEEE Trans. Neural Netw. Learn. Syst. 28, 1889–1901 (2017)

    Article  Google Scholar 

  7. Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)

    Article  Google Scholar 

  8. Lv, M., Wang, C.N., Ren, G.D., et al.: Model of electrical activity in a neuron under magnetic flow effect. Nonlinear Dyn. 85, 1479–1490 (2016)

    Article  Google Scholar 

  9. Mou, J., Sun, K.H., Ruan, J.Y.: A nonlinear circuit with two memcapacitors. Nonlinear Dyn. 86, 1–10 (2016)

    Article  Google Scholar 

  10. Zhou, L., Wang, C.H., Zhou, L.L.: Generating hyperchaotic multi-wing attractor in a 4D memristive circuit. Nonlinear Dyn. 85, 1–11 (2016)

    Article  Google Scholar 

  11. Yu, D.S., Liang, Y., Iu, H.H.C.: Dynamic behavior of coupled memristor circuits. IEEE Trans. Circuits Syst. I(62), 1607–1616 (2015)

    Article  MathSciNet  Google Scholar 

  12. Wang, X.P., Chen, M., Shen, Y.: Switching mechanism for TiO\(_{2}\) memristor and quantitative analysis of exponential model parameters. Chin. Phys. B 24, 088401 (2015)

    Article  Google Scholar 

  13. Sachhidh, K., Naghmeh, K., Ozgur, S., et al.: Security vulnerabilities of emerging nonvolatile main memories and countermeasures. Trans. Comput. Aided Des. Integr. Circuits Syst. 34, 2–15 (2015)

    Article  Google Scholar 

  14. Anas, M., Md, T.R., Domenic, F., Mehdi, A.: Memristor PUF—a security primitive: theory and experiment. IEEE J. Emerg. Sel. Top. Circuits Syst. 5, 222–229 (2015)

    Article  Google Scholar 

  15. Li, C.B., Pehlivan, I., Sprott, J.C., et al.: A novel four-wing strange attractor bornin bistability. IEICE Electron. Lett. 12, 1–12 (2015)

    Google Scholar 

  16. Lai, Q., Chen, S.M.: Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127, 3000–3004 (2016)

    Article  Google Scholar 

  17. Min, F.H., Luo Albert, C.J.: On parameter characteristics of chaotic synchronization in two nonlinear gyroscope systems. Nonlinear Dyn. 69, 1203–1223 (2012)

    Article  MathSciNet  Google Scholar 

  18. Tlelo-Cuautle, E., Fraga, L.G.D.L., Pham, V.T., et al.: Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points. Nonlinear Dyn. 89, 1129–1139 (2017)

    Article  Google Scholar 

  19. Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  20. Bao, B.C., Ma, Z.H., Xu, J.P., et al.: A simple memristor chaotic circuit with complex dynamics. Int. J. Bifurc. Chaos 21, 2629–2645 (2011)

    Article  MATH  Google Scholar 

  21. Bao, B.C., Xu, J.P., Zhou, G.H., et al.: Chaotic memristive circuit: equivalent circuit realization and dynamical analysise. Chin. Phys. B 20, 120502 (2011)

    Article  Google Scholar 

  22. Xu, Q., Lin, Y., Bao, B.C., et al.: Multiple attractors in a non-ideal active voltage-controlled memristor based Chua’s circuit. Chaos Solitons Fractals 83, 186–200 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  23. Chen, M., Li, M.Y., Yu, Q., et al.: Dynamics of self-excited attractors and hidden attractors in generalized memristor-based Chua’s circuit. Nonlinear Dyn. 81, 215–226 (2015)

    Article  MathSciNet  Google Scholar 

  24. Njitacke, Z.T., Kengne, J., Fotsin, H.B., et al.: Coexistence of multiple attractors and crisis route to chaos in a novel memristive diode bidge-based Jerk circuit. Chaos Solitons Fractals 91, 180–197 (2016)

    Article  MATH  Google Scholar 

  25. Yuan, F., Wang, G.Y., Shen, Y.R., et al.: Coexisting attractors in a memcapacitor-based chaotic oscillator. Nonlinear Dyn. 86, 37–50 (2016)

    Article  MathSciNet  Google Scholar 

  26. Ma, J., Wu, F.Q., Ren, G.D., et al.: A class of initials-dependent dynamical systems. Appl. Math. Comput. 298, 65–76 (2017)

    MathSciNet  Google Scholar 

  27. Wang, Z.L., Min, F.H., Wang, E.R.: A new hyperchaotic circuit with two memristors and its application in image encryption. AIP Adv. 6, 095316 (2016)

    Article  Google Scholar 

  28. Adhikari, S.P., Sah, MPd, Kim, H., et al.: Three fingerprints of memristor. IEEE Trans. Circuits Syst. I Regul. Pap. 60, 3008–3021 (2013)

    Article  Google Scholar 

  29. Chua, L.O., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circuits Syst. 33, 1072–1118 (1986)

    Article  MATH  Google Scholar 

  30. Shahzad, M., Pham, V.T., Ahmad, M.A.: Synchronization and circuit design of a chaotic system with coexisting hidden attractors. Eur. Phys. J. 224, 1637–1652 (2015)

    Google Scholar 

  31. Li, C.Q., Chen, M.Z.Q., Lo, K.-T.: Breaking an image encryption algorithm based on chaos. Int. J. Bifurc. Chaos 21, 2067 (2011)

    Article  MATH  Google Scholar 

  32. Li, C.Q., Xie, T., Liu, Q., et al.: Cryptanalyzing image encryption using chaotic logistic map. Nonlinear Dyn. 78, 1545–1551 (2014)

    Article  Google Scholar 

  33. Zhou, G.M., Zhang, D.X., Liu, Y.J., et al.: A novel image encryption algorithm based on chaos and line map. Neurocomputing 169, 150–157 (2015)

  34. Li, C.H., Luo, G.C., Qin, K., et al.: An image encryption scheme based on chaotic tent map. Nonlinear Dyn. 87, 121–133 (2017)

    Google Scholar 

  35. Sun, K.H., Duo, L.A., Dong, Y.: Multiple coexisting attractors and hysteresis in the generalized ueda oscillator. Math. Probl. Eng. 2013, 256092 (2013)

    MATH  Google Scholar 

  36. Bao, B.C., Jiang, T., Xu, Q.: Coexisting infinitely many attractors in active band-pass filter-based memristive circuit. Nonlinear Dyn. 86, 1711–1723 (2016)

    Article  Google Scholar 

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Acknowledgements

This work is supported by the National Nature Science Foundation of China under Grant No. 51475246, the Natural Science Foundation of Jiangsu Province of China under Grant No. Bk20131402 and the Postgraduate Research & Practice Innovation Program of Jiangsu Province of China under Grant No. KYCX17_1082.

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  1. School of Electrical and Automation Engineering, Nanjing Normal University, Nanjing, 210042, China

    Guangya Peng & Fuhong Min

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  1. Guangya Peng
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  2. Fuhong Min
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Correspondence to Fuhong Min.

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Peng, G., Min, F. Multistability analysis, circuit implementations and application in image encryption of a novel memristive chaotic circuit. Nonlinear Dyn 90, 1607–1625 (2017). https://doi.org/10.1007/s11071-017-3752-2

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