Table of Contents Author Guidelines Submit a Manuscript
Mathematical Problems in Engineering
Volume 2011, Article ID 756462, 10 pages
http://dx.doi.org/10.1155/2011/756462
Research Article

How to Generate Chaos from Switching System: A Saddle Focus of Index 1 and Heteroclinic Loop-Based Approach

College of Automation, Guangdong University of Technology, Guangzhou 510006, China

Received 16 July 2011; Accepted 12 September 2011

Academic Editor: Reza Jazar

Copyright © 2011 Fang Bao and Simin Yu. 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. O. Chua, M. Komuro, and T. Matsumoto, “The double scroll family,” IEEE Transactions on Circuits and Systems I, vol. 33, no. 11, pp. 1073–1117, 1986. View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  2. E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  3. G. R. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos, vol. 9, no. 7, pp. 1465–1466, 1999. View at Google Scholar
  4. J. C. Sprott, “A new class of chaotic circuit,” Physics Letters A, vol. 266, no. 1, pp. 19–23, 2000. View at Publisher · View at Google Scholar · View at Scopus
  5. J. C. Sprott, “Simple chaotic systems and circuits,” American Journal of Physics, vol. 68, no. 8, pp. 758–763, 2000. View at Publisher · View at Google Scholar · View at Scopus
  6. T. Zhou and G. Chen, “Classification of chaos in 3-D autonomous quadratic systems-I. Basic framework and methods,” International Journal of Bifurcation and Chaos, vol. 16, no. 9, pp. 2459–2479, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  7. M. E. Yalçin, J. A. K. Suykens, J. Vandewalle, and S. Özouz, “Families of scroll grid attractors,” International Journal of Bifurcation and Chaos, vol. 12, no. 1, pp. 23–41, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. G. Q. Zhong, K. F. Man, and G. Chen, “A systematic approach to generating n-scroll attractors,” International Journal of Bifurcation and Chaos, vol. 12, no. 12, pp. 2907–2915, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. S. Yu, J. Lü, G. Chen, and X. Yu, “Design and implementation of grid multiwing butterfly chaotic attractors from a piecewise Lorenz system,” IEEE Transactions on Circuits and Systems II, vol. 57, no. 10, Article ID 5575404, pp. 803–807, 2010. View at Publisher · View at Google Scholar · View at Scopus
  10. G. Li and X. Chen, “Constructing piecewise linear chaotic system based on the heteroclinic Shil'nikov theorem,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 1, pp. 194–203, 2009. View at Publisher · View at Google Scholar · View at Scopus
  11. S. Yu, J. Lü, G. Chen, and X. Yu, “Generating grid multiwing chaotic attractors by constructing heteroclinic loops into switching systems,” IEEE Transactions on Circuits and Systems II, vol. 58, no. 5, pp. 314–318, 2011. View at Publisher · View at Google Scholar
  12. C. P. Silva, “Shil'nikov's theorem—a tutorial,” IEEE Transactions on Circuits and Systems I, vol. 40, no. 10, pp. 675–682, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus