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International Journal of Analysis
Volume 2013 (2013), Article ID 368150, 3 pages
http://dx.doi.org/10.1155/2013/368150
Research Article

Infinite-Scroll Attractor Generated by the Complex Pendulum Model

Department of Mathematics, Shivaji University, Vidyanagar, Kolhapur 416004, India

Received 20 November 2012; Revised 4 February 2013; Accepted 12 February 2013

Academic Editor: Rodica Costin

Copyright © 2013 Sachin Bhalekar. 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 nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963.
  2. O. E. Rossler, “An equation for continuous chaos,” Physics Letters A, vol. 57, pp. 397–398, 1976.
  3. 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
  4. J. Lü and G. R. 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
  5. 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.
  6. P. Wang, J. Lu, and M. J. Ogorzalek, “Global relative parameter sensitivities of the feed-forward loops in genetic networks,” Neurocomputing, vol. 78, no. 1, pp. 155–165, 2012.
  7. 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
  8. 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
  9. G. M. Mahmoud, A. A. Mohamed, and S. A. Aly, “Strange attractors and chaos control in periodically forced complex Duffing's oscillators,” Physica A, vol. 292, no. 1–4, pp. 193–206, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. Lü and G. Chen, “A time-varying complex dynamical network model and its controlled synchronization criteria,” IEEE Transactions on Automatic Control, vol. 50, no. 6, pp. 841–846, 2005. View at Publisher · View at Google Scholar · View at MathSciNet
  11. J. Lü, X. Yu, G. Chen, and D. Cheng, “Characterizing the synchronizability of small-world dynamical networks,” IEEE Transactions on Circuits and Systems, vol. 51, no. 4, pp. 787–796, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  12. J. Zhu, J. Lu, and X. Yu, “Flocking of multi-agent non-holonomic systems with proximity graphs,” IEEE Transactions on Circuits and Systems I, vol. 60, no. 1, pp. 199–210, 2013.
  13. H. Goldstein, Classical Mechanics, Addison-Wesley, New York, NY, USA, 1980. View at MathSciNet
  14. L. O. Chua, M. Komuro, and T. Matsumoto, “The double scroll family,” IEEE Transactions on Circuits and Systems, vol. 33, no. 11, pp. 1072–1097, 1986. View at Publisher · View at Google Scholar · View at MathSciNet
  15. C. P. Silva, “Shil'cprime nikov's theorem—a tutorial,” IEEE Transactions on Circuits and Systems, vol. 40, no. 10, pp. 675–682, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  16. D. Cafagna and G. Grassi, “New 3D-scroll attractors in hyperchaotic Chua's circuits forming a ring,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 13, no. 10, pp. 2889–2903, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. Lü, G. Chen, X. Yu, and H. Leung, “Design and analysis of multiscroll chaotic attractors from saturated function series,” IEEE Transactions on Circuits and Systems, vol. 51, no. 12, pp. 2476–2490, 2004. View at Publisher · View at Google Scholar · View at MathSciNet