A study on Generalized Synchronization in Hyper-Chaos with SC-CNN

  • Bae, Young-Chul (Division of Electron Communication and Electrical Engineering, Yosu National University) ;
  • Kim, Ju-Wan (Department of Electrical Engineering, Graduate School of Yosu National Universit) ;
  • Song, Hag-Hyun (Institute of Information Technology Assessment(IITA) ;
  • Kim, Yoon-Ho (Department of Computer Engineering., Mok Won University)
  • Published : 2003.12.01


In this paper, we introduce a hyper-chaos synchronization method using hyper-chaos circuit consist of State-Controlled Cellular Neural Network (SC-CNN). We make a hyper-chaos circuit using SC-CNN with the n-double scroll. A hyper-chaos circuit is created by applying identical n-double scroll or non-identical n-double scroll and Chua's oscillator with weak coupled method to each cell. Hyper-chaos synchronization was achieved using GS(Generalized Synchronization) method between the transmitter and receiver about each state variable in the SC-CNN.


Chaos;Hyper-chaos;Generalized Synchronization;Nonlinear Dynamics


  1. K. M. Cuomo, 'Synthesizing Self - Synchronizing Chaotic Arrays', Int. J.Bifurcation and Chaos, vol. 4, no. 3,pp. 727-736,1993 https://doi.org/10.1142/S0218127494000526
  2. L. Kocarev, 'Chaos-based cryptography: A brief overview', IEEE, Vol. pp. 7-21. 2001
  3. P. Arena, S. Baglio, L. Fortuna and G. Maganaro, 'Chua's circuit can be generated by CNN cell', IEEE Trans. Circuit and Systems I, CAS-42, pp. 123-125. 1995
  4. L. O. Chua 'Chua's circuit 10 Years Later', Int. J. Circuit Theory and Application, vol. 22, pp 79-305, 1994
  5. K. M. Short, 'Unmasking a modulated chaotic communications scheme', Int. J. Bifurcation and Chaos, vol. 6, no. 2, pp. 367-375, 1996 https://doi.org/10.1142/S0218127496000114
  6. M. Itoh, K. Komeyama, A. Ikeda and L. O. Chua, 'Chaos Synchronization in Coupled Chua Circuits', IEICE. NLP. 92-51. pp. 33-40. 1992
  7. L. Kocarev, K. S. Halle, K. Eckert and L. O. Chua, 'Expermental Demonstration of Secure Communication via Chaotic Synchronization' Int. J. Bifurcation and Chaos, vol. 2, no. 3, pp. 709-713,1992 https://doi.org/10.1142/S0218127492000823
  8. K. S. Halle, C. W. Wu, M. Itoh and L. O. Chua, 'Spread Spectrum communication through modulation of chaos' Int. J. Bifurcation and Chaos, vol. 3, no. 2, pp.469-477, 1993 https://doi.org/10.1142/S0218127493000374
  9. L. O. Chua, M. Itoh, L. Kocarev, and K. Eckert, 'Chaos Synchronization in Chua's Circuit' J. Circuit. Systems and computers, vol. 3, no. 1, pp. 93-108, 1993 https://doi.org/10.1142/S0218126693000071
  10. J.A.K.Suykens, 'n-Double Scroll Hypercubes in 1-D CNNs' Int. J. Bifurcation and Chaos, vol. 7, no. 8, pp. 1873-1885, 1997 https://doi.org/10.1142/S021812749700145X
  11. P.Arena, P.Baglio, F.Fortuna & G.Manganaro, 'Generation of n-double scrolls via cellular neural networks', Int. J. Circuit Theory Appl, 24, 241-252, 1996 https://doi.org/10.1002/(SICI)1097-007X(199605/06)24:3<241::AID-CTA912>3.0.CO;2-J
  12. J.J. Slotine & W.Li, 'Applied Nonlinear Control', Prentice-Hall, NJ, 1991
  13. M. Itoh, H. Murakami and L. O. Chua, 'Communication System Via Chaotic Modulations' IEICE. Trans. Fundamenrtals. vol. E77-A, no. 6, pp. 1000-1005, 1994
  14. M. Brucoli, D. Cafagna, L. Camimeo & G. Grassi, 'An efficient technique for signal masking using synchronized hyperchaos circuits', Proc. $5^{th}$ Int. workshop on Nonlinear Dynamics of Electronic Systems(NDES '97), Moscow, Russia, June 26-27, pp. 229-232, 1997
  15. L. M. Pecora and T. L. Carroll 'Synchronization in Chaotic System' Phy. Rev. Lett., vol. 64, no. 8, pp. 821-824, 1990 https://doi.org/10.1103/PhysRevLett.64.821
  16. L. Kocarav, L & U. Parlitz, 'Generalized synchronization, predictability and equivalence of unidirectionally coupled dynamical systems', Phys. Rev. Lett, vol. 76, no.11, pp. 1816-1819, 1996 https://doi.org/10.1103/PhysRevLett.76.1816
  17. J.A.k. Suyken, P.F. Curran & L.O. Chua, 'Masterslave synchronization using dynamic output feedback', Int. J. Bifurcation and Chaos, vol. 7, no. 3, 671-679, 1997 https://doi.org/10.1142/S0218127497000467