About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2014 (2014), Article ID 953265, 14 pages
http://dx.doi.org/10.1155/2014/953265
Research Article

Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

1School of Information Science and Engineering, Yunnan University, Kunming 650091, China
2School of Mathematics and Computer Science, Yunnan University of Nationalities, Kunming 650031, China
3Bureau of Asset Management, Yunnan University, Kunming 650091, China

Received 13 August 2013; Revised 25 October 2013; Accepted 30 October 2013; Published 3 February 2014

Academic Editor: Narcisa C. Apreutesei

Copyright © 2014 Xiaobing Zhou 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. A. C. Fowler, M. J. McGuinness, and J. D. Gibbon, “The complex Lorenz equations,” Physica D, vol. 4, no. 2, pp. 139–163, 1981/82. View at Publisher · View at Google Scholar · View at MathSciNet
  2. C. Z. Ning and H. Haken, “Detuned lasers and the complex Lorenz equations: subcritical and supercritical Hopf bifurcations,” Physical Review A, vol. 41, pp. 3826–3837, 1990.
  3. J. D. Gibbon and M. J. McGuinness, “The real and complex Lorenz equations in rotating fluids and lasers,” Physica D, vol. 5, no. 1, pp. 108–122, 1982. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. G. M. Mahmoud and A. A. M. Farghaly, “Chaos control of chaotic limit cycles of real and complex van der Pol oscillators,” Chaos, Solitons and Fractals, vol. 21, no. 4, pp. 915–924, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. G. M. Mahmoud, T. Bountis, and E. E. Mahmoud, “Active control and global synchronization of the complex Chen and Lü systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 17, no. 12, pp. 4295–4308, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. G. M. Mahmoud, T. Bountis, M. A. Al-Kashif, and S. A. Aly, “Dynamical properties and synchronization of complex non-linear equations for detuned lasers,” Dynamical Systems, vol. 24, no. 1, pp. 63–79, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. E. E. Mahmoud, “Dynamics and synchronization of new hyperchaotic complex Lorenz system,” Mathematical and Computer Modelling, vol. 55, no. 7-8, pp. 1951–1962, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. G. M. Mahmoud, M. E. Ahmed, and N. Sabor, “On autonomous and nonautonomous modified hyperchaotic complex Lü systems,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 21, no. 7, pp. 1913–1926, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. G. M. Mahmoud and M. E. Ahmed, “A hyperchaotic complex system generating two-, three-, and four-scroll attractors,” Journal of Vibration and Control, vol. 18, no. 6, pp. 841–849, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  10. 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
  11. G. Chen and X. Dong, From Chaos to Order: Methodologies, Perspectives and Applications, vol. 24, World Scientific Publishing, Singapore, 1998. View at MathSciNet
  12. A. A. Koronovskii, O. I. Moskalenko, and A. E. Hramov, “On the use of chaotic synchronization for secure communication,” Physics-Uspekhi, vol. 52, pp. 1213–1238, 2009.
  13. B. S. Dmitriev, A. E. Hramov, A. A. Koronovskii, A. V. Starodubov, D. I. Trubetskov, and Y. D. Zharkov, “First experimental observation of generalized synchronization phenomena in microwave oscillators,” Physical Review Letters, vol. 102, Article ID 074101, 2009.
  14. M. Hu, Y. Yang, Z. Xu, and L. Guo, “Hybrid projective synchronization in a chaotic complex nonlinear system,” Mathematics and Computers in Simulation, vol. 79, no. 3, pp. 449–457, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. S. Liu and P. Liu, “Adaptive anti-synchronization of chaotic complex nonlinear systems with unknown parameters,” Nonlinear Analysis: Real World Applications, vol. 12, no. 6, pp. 3046–3055, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. E. E. Mahmoud, “Modified projective phase synchronization of chaotic complex nonlinear systems,” Mathematics and Computers in Simulation, vol. 89, pp. 69–85, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  17. G. M. Mahmoud, E. E. Mahmoud, and A. A. Arafa, “On projective synchronization of hyperchaotic complex nonlinear systems based on passive theory for secure communications,” Physica Scripta, vol. 87, no. 5, Article ID 055002, 2013.
  18. X. B. Zhou, M. R. Jiang, and X. M. Cai, “Synchronization of a novel hyperchaotic complex-variable system based on finite-time stability Theory,” Entropy, vol. 15, pp. 4334–4344, 2013.
  19. R. Z. Luo, Y. L. Wang, and S. C. Deng, “Combination synchronization of three classic chaotic systems using active backstepping design,” Chaos, vol. 21, no. 4, Article ID 043114, 2011.
  20. X. B. Zhou, M. R. Jiang, and Y. Q. Huang, “Combination synchronization of three identical or different nonlinear complex hyperchaotic systems,” Entropy, vol. 15, pp. 3746–3761, 2013.
  21. J. Sun, Y. Shen, G. Zhang, C. Xu, and G. Cui, “Combination-combination synchronization among four identical or different chaotic systems,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1211–1222, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  22. G. M. Mahmoud, M. A. Al-Kashif, and A. A. Farghaly, “Chaotic and hyperchaotic attractors of a complex nonlinear system,” Journal of Physics A, vol. 41, no. 5, Article ID 055104, 12 pages, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. G. M. Mahmoud, S. A. Aly, and M. A. AL-Kashif, “Dynamical properties and chaos synchronization of a new chaotic complex nonlinear system,” Nonlinear Dynamics, vol. 51, no. 1-2, pp. 171–181, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. R. Z. Luo and Y. L. Wang, “Finite-time stochastic combination synchronization of three different chaotic systems and its application in secure communication,” Chaos, vol. 22, no. 2, Article ID 023109, 2012.
  25. H. P. Ren, M. S. Baptista, and C. Grebogi, “Wireless communication with chaos,” Physical Review Letters, vol. 110, no. 18, Article ID 184101, 5 pages, 2013.