About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 910189, 6 pages
http://dx.doi.org/10.1155/2013/910189
Research Article

A Fractional-Order Chaotic System with an Infinite Number of Equilibrium Points

1Center of System Theory and Its Applications, Chongqing University of Posts and Telecommunications, Chongqing 400065, China
2Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China

Received 18 February 2013; Accepted 21 March 2013

Academic Editor: Xiao-Song Yang

Copyright © 2013 Ping 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. E. N. Lorenz, “Deterministic nonperodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  2. I. Grigorenko and E. Grigorenko, “Chaotic dynamics of the fractional Lorenz system,” Physical Review Letters, vol. 91, no. 3, Article ID 034101, 4 pages, 2003. View at Scopus
  3. Q. Jia, “Hyperchaos generated from the Lorenz chaotic system and its control,” Physics Letters A, vol. 366, no. 3, pp. 217–222, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. X. Y. Wang and J. M. Song, “Synchronization of the fractional order hyperchaos Lorenz systems with activation feedback control,” Communications in Nonlinear Science and Numerical Simulation, vol. 14, no. 8, pp. 3351–3357, 2009. View at Publisher · View at Google Scholar · View at Scopus
  5. G. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 9, no. 7, pp. 1465–1466, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. C. Li and G. Peng, “Chaos in Chen's system with a fractional order,” Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 443–450, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. Z. Y. Yan, “Controlling hyperchaos in the new hyperchaotic Chen system,” Applied Mathematics and Computation, vol. 168, no. 2, pp. 1239–1250, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. X. J. Wu and Y. Lu, “Generalized projective synchronization of the fractional-order Chen hyperchaotic system,” Nonlinear Dynamics, vol. 57, no. 1-2, pp. 25–35, 2009. View at Publisher · View at Google Scholar · View at Scopus
  9. J. Lü and G. Chen, “A new chaotic attractor coined,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 12, no. 3, pp. 659–661, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. G. Lu, “Chaotic dynamics of the fractional-order Lü system and its synchronization,” Physics Letters A, vol. 354, no. 4, pp. 305–311, 2006. View at Publisher · View at Google Scholar
  11. P. Zhou, R. Ding, and Y. X. Cao, “Multi drive-one response synchronization for fractional-order chaotic systems,” Nonlinear Dynamics, vol. 70, no. 2, pp. 1263–1271, 2012. View at Publisher · View at Google Scholar
  12. Q. Li and X.-S. Yang, “New walking dynamics in the simplest passive bipedal walking model,” Applied Mathematical Modelling, vol. 36, no. 11, pp. 5262–5271, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Q. Li, “A topological horseshoe in the hyperchaotic Rössler attractor,” Physics Letters A, vol. 372, no. 17, pp. 2989–2994, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. Q. Li, X.-S. Yang, and S. Chen, “Hyperchaos in a spacecraft power system,” International Journal of Bifurcation and Chaos, vol. 21, no. 6, pp. 1719–1726, 2011. View at Publisher · View at Google Scholar
  15. S. Dadras, H. R. Momeni, G. Qi, and Z.-l. Wang, “Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form,” Nonlinear Dynamics, vol. 67, no. 2, pp. 1161–1173, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. Z. Ping, C. Yu-Xia, and C. Xue-Feng, “A new hyperchaos system and its circuit simulation by EWB,” Chinese Physics B, vol. 18, no. 4, pp. 1394–1398, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. D. R. Zhu, C. X. Liu, and B. N. Yan, “Controlling and synchronization of hyperchaotic system based on passive control,” Chinese Physics B, vol. 21, no. 9, Article ID 090509, 7 pages, 2012. View at Publisher · View at Google Scholar
  18. J. C. Sprott, “Some simple chaotic flows,” Physical Review E, vol. 50, no. 2, pp. R647–R650, 1994. View at Publisher · View at Google Scholar · View at MathSciNet
  19. M. S. Tavazoei and M. Haeri, “A necessary condition for double scroll attractor existence in fractional-order systems,” Physics Letters A, vol. 367, no. 1-2, pp. 102–113, 2007. View at Publisher · View at Google Scholar · View at Scopus
  20. M. S. Tavazoei and M. Haeri, “Chaos control via a simple fractional-order controller,” Physics Letters A, vol. 372, no. 6, pp. 798–807, 2008. View at Publisher · View at Google Scholar · View at Scopus
  21. X.-Y. Wang, Y.-J. He, and M.-J. Wang, “Chaos control of a fractional order modified coupled dynamos system,” Nonlinear Analysis. Theory, Methods & Applications A, vol. 71, no. 12, pp. 6126–6134, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. C.-M. Chang and H.-K. Chen, “Chaos and hybrid projective synchronization of commensurate and incommensurate fractional-order Chen-Lee systems,” Nonlinear Dynamics, vol. 62, no. 4, pp. 851–858, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. Z. M. Odibat, “Adaptive feedback control and synchronization of non-identical chaotic fractional order systems,” Nonlinear Dynamics, vol. 60, no. 4, pp. 479–487, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. Z. Odibat, “A note on phase synchronization in coupled chaotic fractional order systems,” Nonlinear Analysis. Real World Applications. An International Multidisciplinary Journal, vol. 13, no. 2, pp. 779–789, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet