Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 584954, 10 pages
http://dx.doi.org/10.1155/2015/584954
Research Article

Parametric Controller Design of Hopf Bifurcation System

School of Energy Science and Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611131, China

Received 11 September 2015; Accepted 17 December 2015

Academic Editor: Stefano Lenci

Copyright © 2015 Jinbo Lu 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. E. H. Abed and J.-H. Fu, “Local feedback stabilization and bifurcation control. I. Hopf bifurcation,” Systems & Control Letters, vol. 7, no. 1, pp. 11–17, 1986. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  2. G. Chen and K. Yap, “Feedback control of Hopf bifurcations,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 6, pp. 661–672, 2001. View at Google Scholar
  3. A. Jimenez-Triana, W. K.-S. Tang, G. Chen, and A. Gauthier, “Chaos control in duffing system using impulsive parametric perturbations,” IEEE Transactions on Circuits and Systems, vol. 57, no. 4, pp. 305–309, 2010. View at Publisher · View at Google Scholar · View at Scopus
  4. C. Bi, Y. Xiang, Q. Zhang, and J. Hu, “Simulation study of bifurcation control in synchronous switching converter,” in Proceedings of the International Conference on Communications, Circuits and Systems (ICCCAS '13), vol. 2, pp. 463–466, Chengdu, China, November 2013. View at Publisher · View at Google Scholar
  5. A. R. Phadke, M. Fozdar, K. R. Niazi, N. Mithulananthan, and R. C. Bansal, “New technique for computation of closest Hopf bifurcation point using real-coded genetic algorithm,” IET Generation, Transmission & Distribution, vol. 5, no. 1, pp. 11–18, 2011. View at Publisher · View at Google Scholar · View at Scopus
  6. M. Tomim, B. Lopes, R. Leme et al., “Modified Hopf bifurcation index for power system stability assessment,” IEE Proceedings—Generation, Transmission and Distribution, vol. 152, no. 6, pp. 906–912, 2005. View at Publisher · View at Google Scholar
  7. A. Kavitha and G. Uma, “Experimental verification of Hopf bifurcation in DC–DC Luo converter,” IEEE Transactions on Power Electronics, vol. 23, no. 6, pp. 2878–2883, 2008. View at Publisher · View at Google Scholar
  8. F. Liu, H. O. Wang, and Z.-H. Guan, “Stability analysis and control of bifurcation in a TCP fluid flow model of wireless networks,” in Proceedings of the 10th World Congress on Intelligent Control and Automation (WCICA '12), pp. 1026–1030, IEEE, Beijing, China, July 2012. View at Publisher · View at Google Scholar · View at Scopus
  9. L. Yang, Z. Xu, J. Østergaard, Z. Y. Dong, K. P. Wong, and X. Ma, “Oscillatory stability and eigenvalue sensitivity analysis of a DFIG wind turbine system,” IEEE Transactions on Energy Conversion, vol. 26, no. 1, pp. 328–339, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. K. E. Chlouverakis, K. M. Al-Aswad, I. D. Henning, and M. J. Adams, “Determining laser linewidth parameter from Hopf bifurcation minimum in lasers subject to optical injection,” Electronics Letters, vol. 39, no. 16, pp. 1185–1187, 2003. View at Publisher · View at Google Scholar · View at Scopus
  11. M. Huang, C. K. Tse, S.-C. Wong, C. Wan, and X. Ruan, “Low-frequency hopf bifurcation and its effects on stability margin in three-phase PFC power supplies connected to non-ideal power grid,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 60, no. 12, pp. 3328–3340, 2013. View at Publisher · View at Google Scholar · View at Scopus
  12. P. S. Deivasundari, G. Uma, and R. Santhi, “Experimental verification of Hopf bifurcation in pulse-width modulated inverter fed cage induction motor drive system,” IET Power Electronics, vol. 7, no. 2, pp. 340–349, 2014. View at Publisher · View at Google Scholar · View at Scopus
  13. N. G. Sakellaridis, M. E. Karystianos, and C. D. Vournas, “Homoclinic loop and degenerate hopf bifurcations introduced by load dynamics,” IEEE Transactions on Power Systems, vol. 24, no. 4, pp. 1892–1893, 2009. View at Publisher · View at Google Scholar · View at Scopus
  14. G. Chen, J. L. Moiola, and H. O. Wang, “Bifurcation control: theories, methods, and applications,” International Journal of Bifurcation and Chaos, vol. 10, no. 3, pp. 511–548, 2000. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. F. Liu, G. Xiong, Z.-H. Guan, and H. O. Wang, “Stability analysis and control Hopf bifurcation in a FAST TCP model,” in Proceedings of the 32nd Chinese Control Conference (CCC '13), pp. 1076–1080, Xi'an, China, July 2013. View at Scopus
  16. M. Xiao, W. X. Zheng, and J. Cao, “Hopf bifurcation of an (n + 1)-neuron bidirectional associative memory neural network model with delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 1, pp. 118–132, 2013. View at Publisher · View at Google Scholar · View at Scopus
  17. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  18. T. Yang and X. Chen, “Local L2 gain of Hopf bifurcation stabilization,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 4103–4108, IEEE, Cancún, Mexico, December 2008. View at Publisher · View at Google Scholar · View at Scopus
  19. P. Cai, J.-S. Tang, and Z.-B. Li, “Controlling Hopf bifurcation of a new modified hyperchaotic Lü system,” Mathematical Problems in Engineering, vol. 2015, Article ID 614135, 6 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet
  20. F. Verduzco, J. Alvarez, and A. Carrillo, “Normal form and control of the Hopf bifurcation,” in Proceedings of the American Control Conference (ACC '07), pp. 2358–2363, New York, NY, USA, July 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. Z. Wu and P. Yu, “A method for stability and bifurcation control,” IEEE Transactions on Automatic Control, vol. 51, no. 6, pp. 1019–1023, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  22. Z.-Q. Wu, R. Ding, and Y.-S. Chen, “Classification of parametrically constrained bifurcations,” Applied Mathematics and Mechanics. English Edition, vol. 31, no. 2, pp. 135–142, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  23. K. Cho and T. Miyano, “Chaotic cryptography using augmented lorenz equations aided by quantum key distribution,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 62, no. 2, pp. 478–487, 2015. View at Publisher · View at Google Scholar · View at Scopus
  24. R. Tokunaga, T. Matsumoto, L. O. Chua, and S. Miyama, “The piecewise-linear Lorenz circuit is chaotic in the sense of Shilnikov,” IEEE Transactions on Circuits and Systems, vol. 37, no. 6, pp. 766–786, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  25. S. Yu, J. Lu, X. Yu, and G. Chen, “Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops,” IEEE Transactions on Circuits and Systems, vol. 59, no. 5, pp. 1015–1028, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  26. A. Dwivedi, A. K. Mittal, and S. Dwivedi, “Adaptive synchronisation of diffusionless Lorenz systems and secure communication of digital signals by parameter modulation,” IET Communications, vol. 6, no. 13, pp. 2016–2026, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus