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Complexity
Volume 2017, Article ID 3204073, 16 pages
https://doi.org/10.1155/2017/3204073
Research Article

Improving the Complexity of the Lorenz Dynamics

Department of Physic Electronics, Universidad Politécnica de Madrid, Avenida Complutense No. 30, 28040 Madrid, Spain

Correspondence should be addressed to María Pilar Mareca; se.mpu.sif@acerampm

Received 26 July 2016; Accepted 19 September 2016; Published 10 January 2017

Academic Editor: Michael Small

Copyright © 2017 María Pilar Mareca and Borja Bordel. 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, no. 2, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  2. A. B. Orúe, V. Fernández Mármol, G. Álvarez Marañón et al., “Determination of the parameters for a Lorenz system and application to break the security of two-channel chaotic cryptosystems,” Physics Letters A, vol. 372, no. 34, pp. 5588–5592, 2008. View at Google Scholar
  3. A. Ali-Pacha, N. Hadj-Said, A. M'Hamed, and A. Belgoraf, “Lorenz's attractor applied to the stream cipher (Ali-Pacha generator),” Chaos, Solitons and Fractals, vol. 33, no. 5, pp. 1762–1766, 2007. View at Publisher · View at Google Scholar · View at Scopus
  4. K. M. Cuomo, A. V. Oppenheim, and S. H. Strogatz, “Synchronization of Lorenz-based chaotic circuits with applications to communications,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 40, no. 10, pp. 626–633, 1993. View at Publisher · View at Google Scholar · View at Scopus
  5. E. A. Lee, M. Niknami, T. S. Nouidui, and M. Wetter, “Modeling and simulating cyber-physical systems using CyPhySim,” in Proceedings of the 12th International Conference on Embedded Software, pp. 115–124, IEEE Press, October 2015.
  6. L. M. Pecora, L. Moniz, J. Nichols, and T. L. Carroll, “A unified approach to attractor reconstruction,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 17, no. 1, Article ID 013110, 2016. View at Publisher · View at Google Scholar · View at Scopus
  7. S. Yu and W. K. S. Tang, “Tetrapterous butterfly attractors in modified Lorenz systems,” Chaos, Solitons & Fractals, vol. 41, no. 4, pp. 1740–1749, 2009. View at Publisher · View at Google Scholar · View at Scopus
  8. A. S. Elwakil, S. Ozoguz, and M. P. Kennedy, “Creation of a complex butterfly attractor using a novel Lorenz-type system,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, no. 4, pp. 527–530, 2002. View at Publisher · View at Google Scholar · View at Scopus
  9. C.-X. Liu and L. Liu, “A new three-dimensional autonomous chaotic oscillation system,” Journal of Physics: Conference Series, vol. 96, no. 1, Article ID 012173, 2008. View at Publisher · View at Google Scholar
  10. S. Yu, W. K. S. Tang, J. Lu, and G. Chen, “Generation of n×m-wing lorenz-like attractors from a modified Shimizu-Morioka model,” IEEE Transactions on Circuits and Systems II: Express Briefs, vol. 55, no. 11, pp. 1168–1172, 2008. View at Publisher · View at Google Scholar
  11. O. E. Rössler, “Chaotic oscillations: an example of hyperchaos,” in Nonlinear Oscillations in Biology, vol. 17, pp. 141–156, American Mathematical Society, Providence, RI, USA, 1979. View at Google Scholar · View at MathSciNet
  12. X. Liu, X. S. Shen, and H. Zhang, “Multi-scroll chaotic and hyperchaotic attractors generated from Chen system,” International Journal of Bifurcation and Chaos, vol. 22, no. 2, Article ID 1250033, 15 pages, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. C. L. Koliopanos, I. M. Kyprianidis, I. N. Stouboulos, A. N. Anagnostopoulos, and L. Magafas, “Chaotic behaviour of a fourth-order autonomous electric circuit,” Chaos, Solitons and Fractals, vol. 16, no. 2, pp. 173–182, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. S. Cang, G. Qi, and Z. Chen, “A four-wing hyper-chaotic attractor and transient chaos generated from a new 4-D quadratic autonomous system,” Nonlinear Dynamics, vol. 59, no. 3, pp. 515–527, 2010. View at Publisher · View at Google Scholar · View at Scopus
  15. C.-C. Yang, “Adaptive synchronization of Lü hyperchaotic system with uncertain parameters based on single-input controller,” Nonlinear Dynamics, vol. 63, no. 3, pp. 447–454, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  16. C. Han, S. Yu, and G. Wang, “A sinusoidally driven lorenz system and circuit implementation,” Mathematical Problems in Engineering, vol. 2015, Article ID 706902, 11 pages, 2015. View at Publisher · View at Google Scholar · View at Scopus
  17. K. Sun, X. Liu, C. Zhu, and J. C. Sprott, “Hyperchaos and hyperchaos control of the sinusoidally forced simplified Lorenz system,” Nonlinear Dynamics, vol. 69, no. 3, pp. 1383–1391, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. X. Wang and M. Wang, “A hyperchaos generated from Lorenz system,” Physica A. Statistical Mechanics and Its Applications, vol. 387, no. 14, pp. 3751–3758, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares, and C. S. Zhou, “The synchronization of chaotic systems,” Physics Report, vol. 366, no. 1-2, pp. 1–101, 2002. View at Publisher · View at Google Scholar · View at Scopus
  20. L. M. Pecora and T. L. Carroll, “Synchronization in chaotic systems,” Physical Review Letters, vol. 64, no. 8, pp. 821–824, 1990. View at Publisher · View at Google Scholar · View at Scopus
  21. T. Yoshida, H. Mori, and H. Shigematsu, “Analytic study of chaos of the tent map: band structures, power spectra, and critical behaviors,” Journal of Statistical Physics, vol. 31, no. 2, pp. 279–308, 1983. View at Publisher · View at Google Scholar · View at Scopus
  22. Y. Pomeau and P. Manneville, “Intermittent transition to turbulence in dissipative dynamical systems,” Communications in Mathematical Physics, vol. 74, no. 2, pp. 189–197, 1980. View at Publisher · View at Google Scholar · View at Scopus
  23. C. Li and J. C. Sprott, “Coexisting hidden attractors in a 4-D simplified lorenz system,” International Journal of Bifurcation and Chaos, vol. 24, no. 3, Article ID 1450034, 2014. View at Publisher · View at Google Scholar · View at Scopus
  24. G. Baier and J. S. Thomsen, “Prototypes of attractors in four dimensions,” Physical Review E, vol. 48, no. 6, pp. R4172–R4174, 1993. View at Publisher · View at Google Scholar · View at Scopus
  25. A. Wolf, J. B. Swift, H. L. Swinney, and J. A. Vastano, “Determining Lyapunov exponents from a time series,” Physica D: Nonlinear Phenomena, vol. 16, no. 3, pp. 285–317, 1985. View at Publisher · View at Google Scholar · View at Scopus