Table of Contents
Journal of Nonlinear Dynamics
Volume 2014 (2014), Article ID 842790, 7 pages
http://dx.doi.org/10.1155/2014/842790
Research Article

Parameter Estimation and Hybrid Lag Synchronization in Hyperchaotic Lü Systems

School of Mathematical Sciences, Yancheng Teachers University, Yancheng 224002, China

Received 24 October 2013; Revised 19 February 2014; Accepted 26 February 2014; Published 30 March 2014

Academic Editor: Dibakar Ghosh

Copyright © 2014 Qing Wei and Zuolei Wang. 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. P. van Geert, Dynamic Systems of Development: Change between Complexity and Chaos, Harvester Wheatsheaf, 1994.
  2. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Physics Report, vol. 366, no. 1-2, pp. 1–101, 2002. View at Publisher · View at Google Scholar · View at Scopus
  3. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Scopus
  4. Q.-Y. Wang, Q.-S. Lu, and H.-X. Wang, “Transition to complete synchronization via near-synchronization in two coupled chaotic neurons,” Chinese Physics, vol. 14, no. 11, pp. 2189–2195, 2005. View at Publisher · View at Google Scholar · View at Scopus
  5. Z.-M. Ge and C.-C. Chen, “Phase synchronization of coupled chaotic multiple time scales systems,” Chaos, Solitons and Fractals, vol. 20, no. 3, pp. 639–647, 2004. View at Publisher · View at Google Scholar · View at Scopus
  6. C. Li, X. Liao, and K.-W. Wong, “Lag synchronization of hyperchaos with application to secure communications,” Chaos, Solitons and Fractals, vol. 23, no. 1, pp. 183–193, 2005. View at Publisher · View at Google Scholar · View at Scopus
  7. J. Yang and G. Hu, “Three types of generalized synchronization,” Physics Letters A: General, Atomic and Solid State Physics, vol. 361, no. 4-5, pp. 332–335, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. L. Wang, Z. Yuan, X. Chen, and Z. Zhou, “Lag synchronization of chaotic systems with parameter mismatches,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 2, pp. 987–992, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. E. M. Shahverdiev, S. Sivaprakasam, and K. A. Shore, “Lag synchronization in time-delayed systems,” Physics Letters A: General, Atomic and Solid State Physics, vol. 292, no. 6, pp. 320–324, 2002. View at Publisher · View at Google Scholar · View at Scopus
  10. T.-Y. Chiang, J.-S. Lin, T.-L. Liao, and J.-J. Yan, “Anti-synchronization of uncertain unified chaotic systems with dead-zone nonlinearity,” Nonlinear Analysis: Theory, Methods and Applications, vol. 68, no. 9, pp. 2629–2637, 2008. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Hu and Z. Xu, “A general scheme for Q-S synchronization of chaotic systems,” Nonlinear Analysis: Theory, Methods and Applications, vol. 69, no. 4, pp. 1091–1099, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. Z.-L. Wang and X.-R. Shi, “Chaotic bursting lag synchronization of Hindmarsh-Rose system via a single controller,” Applied Mathematics and Computation, vol. 215, no. 3, pp. 1091–1097, 2009. View at Publisher · View at Google Scholar · View at Scopus
  13. M. M. Al-Sawalha and M. S. M. Noorani, “Anti-synchronization of two hyperchaotic systems via nonlinear control,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3402–3411, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Banerjee and A. R. Chowdhury, “Functional synchronization and its application to secure communications,” International Journal of Modern Physics B, vol. 23, no. 9, pp. 2285–2295, 2009. View at Publisher · View at Google Scholar · View at Scopus
  15. M. Mossa Al-sawalha, M. S. M. Noorani, and M. M. Al-dlalah, “Adaptive anti-synchronization of chaotic systems with fully unknown parameters,” Computers and Mathematics with Applications, vol. 59, no. 10, pp. 3234–3244, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. J. Ma, Q.-Y. Wang, W.-Y. Jin, and Y.-F. Xia, “Control chaos in Hindmarsh-Rose neuron by using intermittent feedback with one variable,” Chinese Physics Letters, vol. 25, no. 10, pp. 3582–3585, 2008. View at Publisher · View at Google Scholar · View at Scopus
  17. Z. Li and D. Xu, “A secure communication scheme using projective chaos synchronization,” Chaos, Solitons and Fractals, vol. 22, no. 2, pp. 477–481, 2004. View at Publisher · View at Google Scholar · View at Scopus
  18. A. N. Njah, “Tracking control and synchronization of the new hyperchaotic Liu system via backstepping techniques,” Nonlinear Dynamics, vol. 61, no. 1-2, pp. 1–9, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. J. H. Park, “Synchronization of Genesio chaotic system via backstepping approach,” Chaos, Solitons and Fractals, vol. 27, no. 5, pp. 1369–1375, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. J. Ma, W.-T. Su, and J.-Z. Gao, “Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model,” Acta Physica Sinica, vol. 59, no. 3, pp. 1554–1561, 2010. View at Google Scholar · View at Scopus
  21. C.-F. Feng, Y. Zhang, J.-T. Sun, W. Qi, and Y.-H. Wang, “Generalized projective synchronization in time-delayed chaotic systems,” Chaos, Solitons and Fractals, vol. 38, no. 3, pp. 743–747, 2008. View at Publisher · View at Google Scholar · View at Scopus
  22. J. Ma, F. Li, L. Huang, and W.-Y. Jin, “Complete synchronization, phase synchronization and parameters estimation in a realistic chaotic system,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3770–3785, 2011. View at Publisher · View at Google Scholar · View at Scopus
  23. Z. Wang, “Chaos synchronization of an energy resource system based on linear control,” Nonlinear Analysis: Real World Applications, vol. 11, no. 5, pp. 3336–3343, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. C. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos, “Various synchronization phenomena in bidirectionally coupled double scroll circuits,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 8, pp. 3356–3366, 2011. View at Publisher · View at Google Scholar · View at Scopus
  25. A. A. Selivanov, J. Lehnert, T. Dahms, P. Hövel, A. L. Fradkov, and E. Schöll, “Adaptive synchronization in delay-coupled networks of Stuart-Landau oscillators,” Physical Review E: Statistical, Nonlinear, and Soft Matter Physics, vol. 85, no. 1, Article ID 016201, 2012. View at Publisher · View at Google Scholar · View at Scopus
  26. D. Ghosh, A. R. Chowdhury, and P. Saha, “Multiple delay Rössler system-Bifurcation and chaos control,” Chaos, Solitons and Fractals, vol. 35, no. 3, pp. 472–485, 2008. View at Publisher · View at Google Scholar · View at Scopus
  27. J.-H. Chen, H.-K. Chen, and Y.-K. Lin, “Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems,” Chaos, Solitons and Fractals, vol. 39, no. 2, pp. 707–716, 2009. View at Publisher · View at Google Scholar · View at Scopus
  28. S. K. Bhowmick, C. Hens, D. Ghosh et al., “Mixed synchronization in chaotic oscillators using scalar coupling,” Physics Letters A: General, Atomic and Solid State Physics, vol. 376, no. 36, pp. 2490–2495, 2012. View at Publisher · View at Google Scholar
  29. Q. Zhang, J. Lü, and S. Chen, “Coexistence of anti-phase and complete synchronization in the generalized Lorenz system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 10, pp. 3067–3072, 2010. View at Publisher · View at Google Scholar · View at Scopus
  30. M.-C. Ho, Y.-C. Hung, and C.-H. Chou, “Phase and anti-phase synchronization of two chaotic systems by using active control,” Physics Letters A: General, Atomic and Solid State Physics, vol. 296, no. 1, pp. 43–48, 2002. View at Publisher · View at Google Scholar · View at Scopus
  31. S. Pang and Y. Liu, “A new hyperchaotic system from the Lü system and its control,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2775–2789, 2011. View at Publisher · View at Google Scholar · View at Scopus