Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 614135, 6 pages
http://dx.doi.org/10.1155/2015/614135
Research Article

Controlling Hopf Bifurcation of a New Modified Hyperchaotic Lü System

1College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
2School of Mathematics and Statistics, Minnan Normal University, Zhangzhou 363000, China

Received 23 October 2014; Revised 3 March 2015; Accepted 11 March 2015

Academic Editor: Michael Vynnycky

Copyright © 2015 Ping Cai 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. G. M. Mahmoud and S. A. Aly, “Periodic attractors of complex damped non-linear systems,” International Journal of Non-Linear Mechanics, vol. 35, no. 2, pp. 309–323, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. W. Li, W. Xu, J. Zhao, and H. Wu, “The study on stationary solution of a stochastically complex dynamical system,” Physica A, vol. 385, no. 2, pp. 465–472, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. G. M. Mahmoud, A. A. Mohamed, and S. A. Aly, “Strange attractors and chaos control in periodically forced complex Duffing's oscillators,” Physica A: Statistical Mechanics and its Applications, vol. 292, no. 1–4, pp. 193–206, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. J. Lu, X. Yu, and G. Chen, “Chaos synchronization of general complex dynamical networks,” Physica A: Statistical Mechanics and Its Applications, vol. 334, no. 1-2, pp. 281–302, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. G.-R. Jiang, B.-G. Xu, and Q.-G. Yang, “Bifurcation control and chaos in a linear impulsive system,” Chinese Physics B, vol. 18, no. 12, pp. 5235–5241, 2009. View at Publisher · View at Google Scholar · View at Scopus
  6. X. D. Wang and L. X. Tian, “Bifurcation analysis and linear control of the Newton-Leipnik system,” Chaos, Solitons and Fractals, vol. 27, no. 1, pp. 31–38, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. C.-X. Liang and J.-S. Tang, “Equilibrium points and bifurcation control of a chaotic system,” Chinese Physics B, vol. 17, no. 1, pp. 135–139, 2008. View at Publisher · View at Google Scholar · View at Scopus
  8. J. S. Tang and Z. L. Chen, “Amplitude control of limit cycle in van der Pol system,” International Journal of Bifurcation and Chaos, vol. 16, no. 2, pp. 487–495, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. J. Tang, F. Han, H. Xiao, and X. Wu, “Amplitude control of a limit cycle in a coupled van der Pol system,” Nonlinear Analysis: Theory, Methods & Applications, vol. 71, no. 7-8, pp. 2491–2496, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. L. H. Nguyen and K.-S. Hong, “Hopf bifurcation control via a dynamic state-feedback control,” Physics Letters A, vol. 376, no. 4, pp. 442–446, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. P. Yu and G. Chen, “Hopf bifurcation control using nonlinear feedback with polynomial functions,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 14, no. 5, pp. 1683–1704, 2004. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. Z. Chen and P. Yu, “Hopf bifurcation control for an internet congestion model,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 15, no. 8, pp. 2643–2651, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. S. H. Liu and J. S. Tang, “Linear feedback control of the Hopf bifurcation in the Langford system,” Acta Physica Sinica, vol. 56, no. 6, pp. 3145–3151, 2007 (Chinese). View at Google Scholar · View at MathSciNet
  14. D. S. Chen, H. O. Wang, and G. Chen, “Anti-control of Hopf bifurcations,” IEEE Transactions on Circuits and Systems. I. Fundamental Theory and Applications, vol. 48, no. 6, pp. 661–672, 2001. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. Z. Cheng, “Anti-control of Hopf bifurcation for Chen's system through washout filters,” Neurocomputing, vol. 73, no. 16–18, pp. 3139–3146, 2010. View at Publisher · View at Google Scholar · View at Scopus
  16. Z. S. Lü and L. X. Duan, “Anti-control of Hopf bifurcation in the chaotic Liu system with symbolic computation,” Chinese Physics Letters, vol. 26, no. 5, Article ID 050504, 2009. View at Publisher · View at Google Scholar
  17. Z. C. Wei and Q. G. Yang, “Anti-control of Hopf bifurcation in the new chaotic system with two stable node-foci,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 422–429, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. H. W. Li and M. Wang, “Hopf bifurcation analysis in a Lorenz-type system,” Nonlinear Dynamics, vol. 71, no. 1-2, pp. 235–240, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. J. H. Lü, T. S. Zhou, G. R. Chen, and S. C. Zhang, “Local bifurcations of the Chen system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 10, pp. 2257–2270, 2002. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. Z.-S. Lü and L.-X. Duan, “Control of codimension-2 Bautin bifurcation in chaotic Lü system,” Communications in Theoretical Physics, vol. 52, no. 4, pp. 631–636, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  21. S. H. Liu and J. S. Tang, “Anti-control of Hopf bifurcation at zero equilibrium of the 4D Qi system,” Acta Physica Sinica, vol. 57, no. 10, pp. 6162–6168, 2008 (Chinese). View at Google Scholar · View at MathSciNet
  22. C. X. Liang, J. S. Tang, S. H. Liu, and F. Han, “Hopf bifurcation control of a hyperchaotic circuit system,” Communications in Theoretical Physics, vol. 52, no. 3, pp. 457–462, 2009. View at Publisher · View at Google Scholar · View at Scopus
  23. W.-G. Sun, Y. Chen, C.-P. Li, and J.-Q. Fang, “Synchronization and bifurcation analysis in coupled networks of discrete-time systems,” Communications in Theoretical Physics, vol. 48, no. 5, pp. 871–876, 2007. View at Publisher · View at Google Scholar · View at Scopus
  24. G. Wang, X. Zhang, Y. Zheng, and Y. Li, “A new modified hyperchaotic Lü system,” Physica A, vol. 371, no. 2, pp. 260–272, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. B. D. Hassard, N. D. Kazarinoff, and Y. Wan, Theory and Applications of Hopf Bifurcation, Cambridge University Press, London, UK, 1981. View at MathSciNet