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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Secure Communication Scheme Based on Synchronization of Non-Identical Hyperchaotic Systems

Journal of Applied Nonlinear Dynamics 9(2) (2020) 273--285 | DOI:10.5890/JAND.2020.06.009

O.I. Olusola$^{1}$, K.S. Oyeleke$^{1}$, U.E. Vincent$^{2}$, A. N. Njah$^{1}$

$^{1}$ Department of Physics, University of Lagos, Lagos, Nigeria

$^{2}$ Department of Physical Sciences, Redeemer’s University, Ede, Osun state, Nigeria

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In this work, a secure communication scheme based on the synchronization of non-identical hyperchaotic systems is considered. Using hyperchaotic Lorenz and L ü as prototype oscillators, a secure communication scheme based on synchronization of different hyperchaotic systems with unknown parameters is presented. The communication scheme consists of a transmitter, which comprises the hyperchaotic carrier and modulator, and a receiver, which comprises the hyperchaotic response and a demodulator. Appropriate controllers and parameter update laws are designed to achieve synchronization between the hyperchaotic drive and hyperchaotic response systems and achieve the estimate of unknown parameters simultaneously. The message signal is recovered by the identified parameter and the corresponding demodulation method. Numerical simulations were performed to show the validity and feasibility of the designed secure communication scheme.


  1. [1]  Pecora, L.M. and Carroll, T.L. (1990), Synchronization in chaotic systems. Phys. Rev. Lett., 64, 821–824.
  2. [2]  Pikovsky, A.S. Rosemblum, M., and Kurths, J. (2001), Synchronization: A universal concept in nonlinearscience, Cambridge University Press, New York.
  3. [3]  Eisencraft, M., Fanganiello, R.D., Grzybowski, J.M.V., Soriano, D.C., Attux, R., Batista, A.M., Macau, E.E.N. Monteiro, L.H.A., Romano, J.M.T., Suyama, R., and Yoneyama, T.(2012), Chaos-based communica- tion systems in non-ideal channels. Communications in Nonlinear Science and Numerical Simulation, 17(12), 4707-4718.
  4. [4]  Ren, H.P., Baptista, M.S., and Grebogi, C. (2013), Wireless communication with chaos, Phys. Rev. Lett., 110, 184101.
  5. [5]  Aguilar-López, R., Martnez-Guerra, R., and Perez-Pinacho, C. (2014), Nonlinear observer for synchroniza- tion of chaotic systems with application to secure data transmission, European Physical Journal, Special Topics, 223, 1541-1548,
  6. [6]  Filali, M.B. and Pierre, B. (2014), On observer-based secure communication design using discrete-time hyperchaotic systems, Communications in Nonlinear Science and Numerical Simulation, 19(5), 1424,1432.
  7. [7]  Gabriel, P. and Hilda, A.C. (1995), Extracting messages masked by chaos, Phys. Rev. Lett., 74, 1970-1973.
  8. [8]  Moskalenko, O.I., Koronovskii, A.A., Hramov, A.E., and Boccaletti, S. (2012), Generalized synchronization in mutually coupled oscillators and complex networks, Phys. Rev. E, 86, 036216.
  9. [9]  Rosenblum, M.G., Pikovsky, A.S. and Kurths, J. (1996), Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76, 1804-1807.
  10. [10]  Mirasso, C.R., Carelli, P.V.,Pereira, T., Matias, F.S., and Copelli, M. (2017), Anticipated and zero-lag synchronization in motifs of delay-coupled systems, Chaos: An Interdisciplinary Journal of Nonlinear Science, 27(11), 114305.
  11. [11]  Mainieri, R. and Rehacek, J. (1999), Projective synchronization in three-dimensional chaotic systems, Phys. Rev. Lett., 82, 3042-3045.
  12. [12]  Farivar, F., Shoorehdeli, M.A., Nekoui, M.A., and Teshnehlab, M. (2011), Generalized projective synchro- nization of uncertain chaotic systems with external disturbance, Expert Systems with Applications, 38(5), 4714-4726.
  13. [13]  Wu, Z., Duan, J., and Fu, X. (2012), Complex projective synchronization in coupled chaotic complex dynamical systems, Nonlinear Dyn., 69, 771–779.
  14. [14]  Si, G.Q., Sun, Z.Y., Zhang, Y.B., and Chen, W.Q. (2012), Projective synchronization of different fractional-order chaotic systems with non-identical orders, Nonlinear Analysis: Real World Applications, 13(4), 1761- 1771.
  15. [15]  Dai, H., Si, G.Q., Jia, L.X., and Zhang, Y.B. (2013), Adaptive generalized function matrix projective lag synchronization between fractional-order and integer-order complex networks with delayed coupling and different dimensions, Physica Scripta, 88(5), 055006.
  16. [16]  Wu, X.J., Fu, Z.Y., and Kurths, J. (2015), A secure communication scheme based generalized function projective synchronization of a new 5d hyperchaotic system, Physica Scripta, 90(4), 045210.
  17. [17]  Uyaroğlu, Y. and Pehlivan, I. (2010), Nonlinear sprott94 case a chaotic equation: Synchronization and masking communication applications, Computers & Electrical Engineering, 36(6), 1093-1100.
  18. [18]  Wu, X.J., Wang, H., and Lu, H.T. (2012), Modified generalized projective synchronization of a new fractional- order hyperchaotic system and its application to secure communication, Nonlinear Analysis: Real World Applications, 13(3), 1441-1450.
  19. [19]  Kaddoum, G., Richardson, F.D., and Gagnon, F. (2013), Design and analysis of a multi-carrier differential chaos shift keying communication system, IEEE Transactions on Communications, 61(8), 3281-3291, August 2013.
  20. [20]  Fu, Y.Q., Li, X.Y., Li, Y.N., Yang, W., and Song, H.L. (2013), Chaos m-ary modulation and demodulation method based on hamilton oscillator and its application in communication, Chaos: An Interdisciplinary Journal of Nonlinear Science, 23(1), 013111.
  21. [21]  Vilardy, J.M., Jimenez, C.J., and Perez, R. (2017) Image encryption using the gyrator transform and random phase masks generated by using chaos, Journal of Physics: Conference Series, 850(1), 012012.
  22. [22]  Wang, Y., Zheng, G.Y., and Liu, J.B. (2007), A new four-dimensional hyperchaotic lorenz system, J. Acta Phys. Sinca, 56(6), 3113-3120.
  23. [23]  Wang, F.Q. and Liu, C.X. (2006), Hyperchaos evolved from the liu chaotic system, Chinese Physics, 15, 963-968.
  24. [24]  Strogatz, S.H. (1994) Nonlinear dyamics and chaos (with applications to physics, biology, chemistry and engineering), Westview press, U.S.A.