Nonlinear Dynamics

, Volume 90, Issue 3, pp 1607–1625 | Cite as

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

  • Guangya Peng
  • Fuhong MinEmail author
Original Paper


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.


Memristive chaotic circuit Coexistence of multiple states Circuit model Image encryption 



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.


  1. 1.
    Chua, L.O.: Memristor-the missing circuit element. IEEE Trans. Circuit Theory 18, 507–519 (1971)CrossRefGoogle Scholar
  2. 2.
    Strukov, D.B., Snider, G.S., Stewart, D.R.: The missing memristor found. Nature 453, 80–83 (2008)CrossRefGoogle Scholar
  3. 3.
    Yang, J.J., Strukov, D.B., Stewart, D.R.D.: Memristive devices for computing. Nat. Nanotechnol. 8, 13–24 (2012)CrossRefGoogle Scholar
  4. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 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)CrossRefGoogle Scholar
  7. 7.
    Lv, M., Ma, J.: Multiple modes of electrical activities in a new neuron model under electromagnetic radiation. Neurocomputing 205, 375–381 (2016)CrossRefGoogle Scholar
  8. 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)CrossRefGoogle Scholar
  9. 9.
    Mou, J., Sun, K.H., Ruan, J.Y.: A nonlinear circuit with two memcapacitors. Nonlinear Dyn. 86, 1–10 (2016)CrossRefGoogle Scholar
  10. 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)CrossRefGoogle Scholar
  11. 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)MathSciNetCrossRefGoogle Scholar
  12. 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)CrossRefGoogle Scholar
  13. 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)CrossRefGoogle Scholar
  14. 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)CrossRefGoogle Scholar
  15. 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. 16.
    Lai, Q., Chen, S.M.: Research on a new 3D autonomous chaotic system with coexisting attractors. Optik 127, 3000–3004 (2016)CrossRefGoogle Scholar
  17. 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)MathSciNetCrossRefGoogle Scholar
  18. 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)CrossRefGoogle Scholar
  19. 19.
    Itoh, M., Chua, L.O.: Memristor oscillators. Int. J. Bifurc. Chaos 18, 3183–3206 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 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)CrossRefzbMATHGoogle Scholar
  21. 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)CrossRefGoogle Scholar
  22. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 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)MathSciNetCrossRefGoogle Scholar
  24. 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)CrossRefzbMATHGoogle Scholar
  25. 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)MathSciNetCrossRefGoogle Scholar
  26. 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)MathSciNetGoogle Scholar
  27. 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)CrossRefGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. 29.
    Chua, L.O., Komuro, M., Matsumoto, T.: The double scroll family. IEEE Trans. Circuits Syst. 33, 1072–1118 (1986)CrossRefzbMATHGoogle Scholar
  30. 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. 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)CrossRefzbMATHGoogle Scholar
  32. 32.
    Li, C.Q., Xie, T., Liu, Q., et al.: Cryptanalyzing image encryption using chaotic logistic map. Nonlinear Dyn. 78, 1545–1551 (2014)CrossRefGoogle Scholar
  33. 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)Google Scholar
  34. 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. 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)zbMATHGoogle Scholar
  36. 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)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.School of Electrical and Automation EngineeringNanjing Normal UniversityNanjingChina

Personalised recommendations