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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 213694, 17 pages
http://dx.doi.org/10.1155/2014/213694
Research Article

Nonlinear Dynamic Analysis and Synchronization of Four-Dimensional Lorenz-Stenflo System and Its Circuit Experimental Implementation

Graduate Institute of Automation and Control, National Taiwan University of Science and Technology, No. 43, Section 4, Keelung Road, Taipei 106, Taiwan

Received 2 April 2014; Accepted 25 May 2014; Published 7 August 2014

Academic Editor: Xiao He

Copyright © 2014 Cheng-Hsiung Yang and Cheng-Lin Wu. 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. Z. Li, Y. Soh, and C. Wen, Switched and Impulsive Systems, Analysis, Design, and Applications, vol. 313, Springer, Berlin, Germany, 2005. View at MathSciNet
  2. P. Galajda and D. Kocur, “Chua's circuit in spread spectrum communication systems,” Radio Engineering, vol. 11, no. 2, pp. 6–10, 2002.
  3. L. Kocarev, Z. Galias, and S. Lian, Eds., Intelligent Computing Based on Chaos, vol. 184 of Studies in Computational Intelligence, Springer, Berlin, Germany, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  4. K. Grygiel and P. Szlachetka, “Lyapunov exponents analysis of autonomous and nonautonomous sets of ordinary differential equations,” Acta Physica Polonica B, vol. 26, no. 8, pp. 1321–1331, 1995. View at Zentralblatt MATH · View at MathSciNet
  5. S. H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Perseus Books, Cambridge, Mass, USA, 1994.
  6. K. Kiers, D. Schmidt, and J. C. Sprott, “Precision measurements of a simple chaotic circuit,” American Journal of Physics, vol. 72, no. 4, pp. 503–509, 2004. View at Publisher · View at Google Scholar · View at Scopus
  7. E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, pp. 130–141, 1963.
  8. L. Stenflo, “Generalized Lorenz equations for acoustic-gravity waves in the atmosphere,” Physica Scripta, vol. 53, no. 1, pp. 83–84, 1996. View at Scopus
  9. J. C. Xavier and P. C. Rech, “Regular and chaotic dynamics of the Lorenz-Stenflo system,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 1, pp. 145–152, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. P. Wang, D. Li, and Q. Hu, “Bounds of the hyper-chaotic Lorenz-Stenflo system,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 9, pp. 2514–2520, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. H. Li, X. Liao, and X. Lei, “Two fuzzy control schemes for Lorenz-Stenflo chaotic system,” Journal of Vibration and Control, vol. 18, no. 11, pp. 1675–1682, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  12. W. Xiang, “Equilibrium points and bifurcation control for Lorenz-Stenflo system,” ICIC Express Letters, vol. 3, no. 1, pp. 61–66, 2009. View at Scopus
  13. C.-H. Yang, “Chaos hybrid generalized synchronization of liu-chen system by GYC partial region stability theory,” Journal of Computational and Theoretical Nanoscience, vol. 10, no. 4, pp. 825–831, 2013. View at Publisher · View at Google Scholar · View at Scopus
  14. Z.-M. Ge and C.-H. Yang, “The generalized synchronization of a Quantum-CNN chaotic oscillator with different order systems,” Chaos, Solitons and Fractals, vol. 35, no. 5, pp. 980–990, 2008. View at Publisher · View at Google Scholar · View at Scopus
  15. Z.-M. Ge, C.-W. Yao, and H.-K. Chen, “Stability on partial region in dynamics,” Journal of the Chinese Society of Mechanical Engineers, vol. 15, no. 2, pp. 140–151, 1994. View at Scopus
  16. Z.-M. Ge, J.-K. Yu, and H.-K. Chen, “Three asymptotical stability theorems on partial region with applications,” Japanse Journal of Applied Physics, vol. 37, article 2762, 1998. View at Publisher · View at Google Scholar
  17. P. Frederickson, J.-L. Kaplan, E.-D. Yorke, and J.-A. Yorke, “The Liapunov dimension of strange attractors,” Journal of Differential Equations, vol. 49, no. 2, pp. 185–207, 1983. View at Publisher · View at Google Scholar · View at MathSciNet
  18. X. Wang and G. A. Chen, “A chaotic system with only one stable equilibrium,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 3, pp. 1264–1272, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  19. Y. Liu, “Circuit implementation and finite-time synchronization of the 4D Rabinovich hyperchaotic system,” Nonlinear Dynamics, vol. 67, no. 1, pp. 89–96, 2012. View at Publisher · View at Google Scholar · View at Scopus
  20. A. G. Radwan, A. M. Soliman, and A. L. El-Sedeek, “MOS realization of the double-scroll-like chaotic equation’’,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, no. 2, pp. 285–288, 2003. View at Publisher · View at Google Scholar
  21. A. Abooee, H. A. Yaghini-Bonabi, and M. R. Jahed-Motlagh, “Analysis and circuitry realization of a novel three-dimensional chaotic system,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 5, pp. 1235–1245, 2013. View at Publisher · View at Google Scholar · View at MathSciNet