Table of Contents
Journal of Chaos
Volume 2014 (2014), Article ID 429809, 15 pages
http://dx.doi.org/10.1155/2014/429809
Research Article

Theoretical Analysis and Adaptive Synchronization of a 4D Hyperchaotic Oscillator

1Laboratoire de Mécanique et de Modélisation des Systèmes Physiques (L2MSP), Faculty of Science, University of Dschang, P.O. Box 69 Dschang, Cameroon
2Laboratoire d’Electronique et de Traitement de Signal (LETS), Faculty of Science, University of Dschang, P.O. Box 67 Dschang, Cameroon
3Laboratoire d’Automatique et Informatique Appliquée (LAIA), IUT-FV Bandjoun, University of Dschang, P.O. Box 67 Dschang, Cameroon

Received 31 October 2013; Accepted 14 January 2014; Published 27 February 2014

Academic Editor: Qingdu Li

Copyright © 2014 T. Fonzin Fozin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Matsumoto, L. O. Chua, and K. Kobayashi, “Hyperchaos: laboratory experiment and numerical confirmation,” IEEE Transactions on Circuits and Systems, vol. 33, no. 11, pp. 1143–1147, 1986. View at Google Scholar · View at Scopus
  2. A. Tamaševičius, A. Namajunas, and A. Čenys, “Simple 4D chaotic oscillator,” Electronics Letters, vol. 32, no. 11, pp. 957–958, 1996. View at Google Scholar · View at Scopus
  3. A. Tamaševičius, A. Čenys, G. Mykolaitis, A. Namajunas, and E. Lindberg, “Hyperchaotic oscillator with gyrators,” Electronics Letters, vol. 33, no. 7, pp. 542–544, 1997. View at Google Scholar · View at Scopus
  4. G. Grassi and S. Mascolo, “Synchronisation of hyperchaotic oscillators using a scalar signal,” Electronics Letters, vol. 34, no. 5, pp. 424–425, 1998. View at Google Scholar · View at Scopus
  5. C. P. Silva and A. M. Young, “Introduction to chaos-based communications and signal processing,” in Proceedings of the 2000 IEEE Aerospace Conference, vol. 1, pp. 279–299, March 2000. View at Scopus
  6. B. Cannas and S. Cincotti, “Hyperchaotic behaviour of two bi-directionally coupled Chua's circuits,” International Journal of Circuit Theory and Applications, vol. 30, no. 6, pp. 625–637, 2002. View at Publisher · View at Google Scholar · View at Scopus
  7. N. Goldenfeld and L. P. Kadanoff, “Simple lessons from complexity,” Science, vol. 284, no. 5411, pp. 87–89, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. R. Vicente, J. Daudén, P. Colet, and R. Toral, “Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop,” IEEE Journal of Quantum Electronics, vol. 41, no. 4, pp. 541–548, 2005. View at Publisher · View at Google Scholar · View at Scopus
  9. R. Stoop, J. Peinke, J. Parisi, B. Röhricht, and R. P. Huebener, “A p-Ge semiconductor experiment showing chaos and hyperchaos,” Physica D, vol. 35, no. 3, pp. 425–435, 1989. View at Google Scholar · View at Scopus
  10. Y. Li, W. K. S. Tang, and G. Chen, “Hyperchaos evolved from the generalized Lorenz equation,” International Journal of Circuit Theory and Applications, vol. 33, no. 4, pp. 235–251, 2005. View at Publisher · View at Google Scholar · View at Scopus
  11. Y. Li, X. Liu, G. Chen, and X. Liao, “A new hyperchaotic Lorenz-type system: generation, analysis, and implementation,” International Journal of Circuit Theory and Applications, vol. 39, no. 8, pp. 865–879, 2011. View at Publisher · View at Google Scholar · View at Scopus
  12. C. K. Duan and S. S. Yang, “Synchronizing hyperchaos with a scalar signal by parameter controlling,” Physics Letters A, vol. 229, no. 3, pp. 151–155, 1997. View at Google Scholar · View at Scopus
  13. Z. Liu, C. Liu, M. Ho, Y. Hung, T. Hsu, and I. Jiang, “Synchronization of uncertain hyperchaotic and chaotic systems by adaptive control,” International Journal of Bifurcation and Chaos, vol. 18, no. 12, pp. 3731–3736, 2008. View at Publisher · View at Google Scholar · View at Scopus
  14. J. H. Peng, E. J. Ding, M. Ding, and W. Yang, “Synchronizing hyperchaos with a scalar transmitted signal,” Physical Review Letters, vol. 76, no. 6, pp. 904–907, 1996. View at Google Scholar · View at Scopus
  15. A. Tamasevicius and A. Cenys, “Synchronizing hyperchaos with a single variable,” Physical Review E, vol. 55, pp. 297–299, 1997. View at Google Scholar
  16. A. Tamaševičius, A. Čenys, A. Namajunas, and G. Mykolaitis, “Synchronising hyperchaos in infinite-dimensional dynamical systems,” Chaos, Solitons and Fractals, vol. 9, no. 8, pp. 1403–1408, 1999. View at Google Scholar · View at Scopus
  17. K. Murali, A. Tamasevicius, G. Mykolaitis, A. Namajunas, and E. Lindberg, “Hyperchaos system with unstable oscillators,” Nonlinear Phenomenon in Complex Systems, vol. 3, pp. 7–10, 2000. View at Google Scholar
  18. S. Effati, J. Saberi-Nadjafi, and H. Saberi Nick, “Optimal and adaptive control for a kind of 3D chaotic and 4D hyperchaotic systems,” Applied Mathematical Modelling, vol. 38, pp. 759–774, 2014. View at Google Scholar
  19. D. A. Miller and G. Grassi, “Experimental realization of observer-based hyperchaos synchronization,” IEEE Transactions on Circuits and Systems I, vol. 48, no. 3, pp. 366–374, 2001. View at Publisher · View at Google Scholar · View at Scopus
  20. V. S. Udaltsov, J. Goedgebuer, L. Larger, and W. T. Rhodes, “Communicating with optical hyperchaos: information encryption and decryption in delayed nonlinear feedback systems,” Physical Review Letters, vol. 86, no. 9, pp. 1892–1895, 2001. View at Publisher · View at Google Scholar · View at Scopus
  21. A. Buscarino, L. Fortuna, and M. Frasca, “Experimental robust synchronization of hyperchaotic circuits,” Physica D, vol. 238, no. 18, pp. 1917–1922, 2009. View at Publisher · View at Google Scholar · View at Scopus
  22. C. C. Yang, “Adaptive single input control for synchronization of a 4D Lorenz-Stenflo chaotic system,” Arabian Journal for Science and Engineering, 2013. View at Publisher · View at Google Scholar
  23. G. Pérez and H. A. Cerdeira, “Extracting messages masked by chaos,” Physical Review Letters, vol. 74, no. 11, pp. 1970–1973, 1995. View at Publisher · View at Google Scholar · View at Scopus
  24. L. Pocora, “Hyperchaos harnessed,” Physics World, vol. 9, no. 5, p. 17, 1996. View at Google Scholar · View at Scopus
  25. G. Qi, M. A. van Wyk, B. J. van Wyk, and G. Chen, “A new hyperchaotic system and its circuit implementation,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2544–2549, 2009. View at Publisher · View at Google Scholar · View at Scopus
  26. L. Liu, C. Liu, and Y. Zhang, “Theoretical analysis and circuit implementation of a novel complicated hyperchaotic system,” Nonlinear Dynamics, vol. 66, no. 4, pp. 707–715, 2011. View at Publisher · View at Google Scholar · View at Scopus
  27. W. Wu, Z. Chen, and Z. Yuan, “The evolution of a novel four-dimensional autonomous system: among 3-torus, limit cycle, 2-torus, chaos and hyperchaos,” Chaos, Solitons and Fractals, vol. 39, no. 5, pp. 2340–2357, 2009. View at Google Scholar · View at Scopus
  28. G. Grassi and S. Mascolo, “Nonlinear observer design to synchronize hyperchaotic systems via a scalar signal,” IEEE Transactions on Circuits and Systems I, vol. 44, no. 10, pp. 1011–1013, 1997. View at Google Scholar · View at Scopus
  29. X. Wang and Y. Wang, “Adaptive control for synchronization of a four-dimensional chaotic system via a single variable,” Nonlinear Dynamics, vol. 65, no. 3, pp. 311–316, 2011. View at Publisher · View at Google Scholar · View at Scopus
  30. C. Yang, “Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller,” Nonlinear Dynamics, vol. 63, no. 3, pp. 447–454, 2011. View at Publisher · View at Google Scholar · View at Scopus
  31. A. Tamaševičius, G. Mykolaitis, A. Čenys, and A. Namajunas, “Synchronisation of 4D hyperchaotic oscillators,” Electronics Letters, vol. 32, no. 17, pp. 1536–1538, 1996. View at Google Scholar · View at Scopus
  32. J. Kengne, J. C. Chedjou, V. A. Fono, and K. Kyamakya, “On the analysis of bipolar transistor based chaotic circuits: case of a two-stage colpitts oscillator,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1247–1260, 2012. View at Publisher · View at Google Scholar · View at Scopus
  33. J. Kengne, J. C. Chedjou, G. Kenne, and K. Kyamakya, “Dynamical properties and chaos synchronization of improved Colpitts oscillators,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 7, pp. 2914–2923, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. A. S. Sedra and C. S. Kenneth, Microelectronic Circuits, Oxford University Press, New York, NY, USA, 5th edition, 2003.
  35. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D, vol. 16, no. 3, pp. 285–317, 1985. View at Google Scholar · View at Scopus
  36. K. Giannakopoulos, T. Deliyannis, and J. Hadjidemetriou, “Means for detecting chaos and hyperchaos in nonlinear electronic circuits,” in Proceedings of the 14th IEEE International Conference on Digital Signal Processing, pp. 951–954, 2002.
  37. H. B. Fotsin and P. Woafo, “Adaptive synchronization of a modified and uncertain chaotic Van der Pol-Duffing oscillator based on parameter identification,” Chaos, Solitons and Fractals, vol. 24, no. 5, pp. 1363–1371, 2005. View at Publisher · View at Google Scholar · View at Scopus
  38. Y. Xu, W. Zhou, J. Fang, and W. Sun, “Adaptive bidirectionally coupled synchronization of chaotic systems with unknown parameters,” Nonlinear Dynamics, vol. 66, no. 1-2, pp. 67–76, 2011. View at Publisher · View at Google Scholar · View at Scopus
  39. H. Adloo and M. Roopaei, “Review article on adaptive synchronization of chaotic systems with unknown parameters,” Nonlinear Dynamics, vol. 65, no. 1-2, pp. 141–159, 2011. View at Publisher · View at Google Scholar · View at Scopus
  40. S. Vaidyanathan, “Analysis, control and synchronization of hyperchaotic Zhou system via adaptive control,” Advances in Computing and Information Technology, vol. 117, pp. 1–10, 2013. View at Google Scholar
  41. X. Zhou, L. Xiong, and X. Cai, “Adaptive switched generalized function projective synchronization between two hyperchaotic systems with unknown parameters,” Entropy, vol. 16, pp. 377–388, 2014. View at Google Scholar
  42. X. Zhou, Z. Fan, D. Zhou, and X. Cai, “Passivity-based adaptive hybrid synchronization of a new hyperchaotic system with uncertain parameters,” The Scientific World Journal, vol. 2012, Article ID 920170, 6 pages, 2012. View at Publisher · View at Google Scholar