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Mathematical Problems in Engineering
Volume 2013, Article ID 751616, 10 pages
http://dx.doi.org/10.1155/2013/751616
Research Article

Impulsive Synchronization and Adaptive-Impulsive Synchronization of a Novel Financial Hyperchaotic System

1College of Computer and Information Engineering, Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475004, China
2Department of Software, Institute of Intelligent Network System, Henan University, Kaifeng 475004, China

Received 7 May 2013; Revised 16 July 2013; Accepted 17 July 2013

Academic Editor: Wang Xing-yuan

Copyright © 2013 Xiuli Chai 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. 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 Zentralblatt MATH · View at MathSciNet
  2. X. Wu and H. Lu, “Adaptive generalized function projective lag synchronization of different chaotic systems with fully uncertain parameters,” Chaos, Solitons and Fractals, vol. 44, no. 10, pp. 802–810, 2011. View at Publisher · View at Google Scholar · View at Scopus
  3. X. L. Chai, Z. H. Gan, and C. X. Shi, “Adaptive modified function projective lag synchronization of uncertain hyperchaotic dynamical systems with the same or different dimension and structure,” Mathematical Problems in Engineering, vol. 2013, Article ID 282064, 15 pages, 2013. View at Publisher · View at Google Scholar
  4. D. Lin and X. Wang, “Self-organizing adaptive fuzzy neural control for the synchronization of uncertain chaotic systems with random-varying parameters,” Neurocomputing, vol. 74, no. 12-13, pp. 2241–2249, 2011. View at Publisher · View at Google Scholar · View at Scopus
  5. W. He and J. Cao, “Exponential synchronization of hybrid coupled networks with delayed coupling,” IEEE Transactions on Neural Networks, vol. 21, no. 4, pp. 571–583, 2010. View at Publisher · View at Google Scholar · View at Scopus
  6. S. A. Mohseni and A. H. Tan, “Optimization of neural networks using variable structure systems,” IEEE Transactions on Systems Man and Cybernetics B, vol. 42, no. 6, pp. 1645–1653, 2012. View at Google Scholar
  7. F. W. Fu and S. M. Vander, “Structure-aware stochastic control for transmission scheduling,” IEEE Transactions on Vehicular Technology, vol. 61, no. 9, pp. 3931–3945, 2012. View at Google Scholar
  8. T. Wang, X. Wang, and M. Wang, “A simple criterion for impulsive chaotic synchronization,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 3, pp. 1464–1468, 2011. View at Publisher · View at Google Scholar · View at Scopus
  9. X. Wang and M. Wang, “Impulsive synchronization of hyperchaotic LÜ system,” International Journal of Modern Physics B, vol. 25, no. 27, pp. 3671–3678, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. M. Yang, Y.-W. Wang, J.-W. Xiao, and Y. Huang, “Robust synchronization of singular complex switched networks with parametric uncertainties and unknown coupling topologies via impulsive control,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 11, pp. 4404–4416, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. Ö. Morgül and M. Feki, “Synchronization of chaotic systems by using occasional coupling,” Physical Review E, vol. 55, no. 5A, pp. 5004–5010, 1997. View at Google Scholar · View at Scopus
  12. R. E. Amritkar and N. Gupte, “Synchronization of chaotic orbits: the effect of a finite time step,” Physical Review E, vol. 47, no. 6, pp. 3889–3895, 1993. View at Publisher · View at Google Scholar · View at Scopus
  13. T. Yang and L. O. Chua, “Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication,” IEEE Transactions on Circuits and Systems I, vol. 44, no. 10, pp. 976–988, 1997, Special issue on chaos synchronization, control, and applications. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. Sun and Y. Zhang, “Impulsive control and synchronization of Chua's oscillators,” Mathematics and Computers in Simulation, vol. 66, no. 6, pp. 499–508, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. Z. Luo, “Impulsive control and synchronization of a new chaotic system,” Acta Physica Sinica, vol. 56, no. 10, pp. 5655–5660, 2007. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. C. Ma and X. Wang, “Impulsive control and synchronization of a new unified hyperchaotic system with varying control gains and impulsive intervals,” Nonlinear Dynamics, vol. 70, no. 1, pp. 551–558, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  17. X. Y. Wang, Y. L. Zhang, D. Lin et al., “Impulsive synchronisation of a class of fractional-order hyperchaotic systems,” Chinese Physics B, vol. 20, no. 3, pp. 030506-1–030506-7, 2011. View at Google Scholar
  18. C. L. Li, Y. N. Tong, and H. M. Li, “Adaptive impulsive synchronization of a class of chaotic and hyperchaotic systems,” Physica Scripta, vol. 86, no. 5, Article ID 055003, 2012. View at Google Scholar
  19. Y.-S. Chen and C.-C. Chang, “Adaptive impulsive synchronization of nonlinear chaotic systems,” Nonlinear Dynamics, vol. 70, no. 3, pp. 1795–1803, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  20. X. Wan and J. Sun, “Adaptive-impulsive synchronization of chaotic systems,” Mathematics and Computers in Simulation, vol. 81, no. 8, pp. 1609–1617, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. G. Cai, P. Hu, and Y. Li, “Modified function lag projective synchronization of a financial hyperchaotic system,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1457–1464, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. V. Lakshmikantham, D. D. Baĭnov, and P. S. Simeonov, Theory of Impulsive Differential Equations, World Scientific, Singapore, 1989.
  23. Y. Lin, Y. Chen, and Q. Cao, “Nonlinear and chaotic analysis of a financial complex system,” Applied Mathematics and Mechanics, vol. 31, no. 10, pp. 1305–1316, 2010. View at Publisher · View at Google Scholar · View at Scopus
  24. V. Chellaboina, S. P. Bhat, and W. M. Haddad, “An invariance principle for nonlinear hybrid and impulsive dynamical systems,” Nonlinear Analysis A, vol. 53, no. 3-4, pp. 527–550, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. Z. Q. Zhu and H. P. Hu, “Robust synchronization by time-varying impulsive control,” IEEE Transactions on Circuits and Systems I, vol. 57, no. 9, pp. 735–739, 2010. View at Google Scholar
  26. W. Xie, C. Wen, and Z. Li, “Impulsive control for the stabilization and synchronization of Lorenz systems,” Physics Letters A, vol. 275, no. 1-2, pp. 67–72, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  27. H. Du, Q. Zeng, and N. Lü, “A general method for modified function projective lag synchronization in chaotic systems,” Physics Letters A, vol. 374, no. 13-14, pp. 1493–1496, 2010. View at Publisher · View at Google Scholar · View at Scopus
  28. H. Liu, H. J. Yu, and W. Xiang, “Modified function projective lag synchronization for multi-scroll chaotic system with unknown disturbance,” Acta Physica Sinica, vol. 61, no. 18, Article ID 180503, 2012. View at Google Scholar
  29. H. Du, “Adaptive open-plus-closed-loop control method of modified function projective synchronization in complex networks,” International Journal of Modern Physics C, vol. 22, no. 12, pp. 1393–1407, 2011. View at Publisher · View at Google Scholar · View at Scopus