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Complexity
Volume 2017, Article ID 7520590, 6 pages
https://doi.org/10.1155/2017/7520590
Research Article

Analysis of a Generalized Lorenz–Stenflo Equation

1College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067, China
2Mathematical Postdoctoral Station, College of Mathematics and Statistics, Southwest University, Chongqing 400716, China
3Information Office, Chongqing Technology and Business University, Chongqing 400067, China

Correspondence should be addressed to Rui Chen; moc.qq@5386779721

Received 20 September 2017; Accepted 26 November 2017; Published 13 December 2017

Academic Editor: Giacomo Innocenti

Copyright © 2017 Fuchen Zhang 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 nonperiodic flow,” Journal of the Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963. View at Publisher · View at Google Scholar
  2. G. A. Leonov and N. V. Kuznetsov, “On differences and similarities in the analysis of Lorenz, Chen, and LU systems,” Applied Mathematics and Computation, vol. 256, pp. 334–343, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. 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
  4. G. A. Leonov, “General existence conditions of homoclinic trajectories in dissipative systems. Lorenz, Shimizu-Morioka, LU and Chen systems,” Physics Letters A, vol. 376, no. 45, pp. 3045–3050, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. F. Zhang and G. Zhang, “Further results on ultimate bound on the trajectories of the Lorenz system,” Qualitative Theory of Dynamical Systems, vol. 15, no. 1, pp. 221–235, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. G. A. Leonov, “Bounds for attractors and the existence of homoclinic orbits in the lorenz system,” Journal of Applied Mathematics and Mechanics, vol. 65, no. 1, pp. 19–32, 2001. View at Publisher · View at Google Scholar · View at Scopus
  7. G. A. Leonov, A. I. Bunin, and N. Koksch, “Attraktorlokalisierung des Lorenz-Systems,” Zeitschrift für Angewandte Mathematik und Mechanik. Ingenieurwissenschaftliche Forschungsarbeiten, vol. 67, no. 12, pp. 649–656, 1987. View at Publisher · View at Google Scholar · View at MathSciNet
  8. F. Zhang, C. Mu, S. Zhou, and P. Zheng, “New results of the ultimate bound on the trajectories of the family of the Lorenz systems,” Discrete and Continuous Dynamical Systems - Series B, vol. 20, no. 4, pp. 1261–1276, 2015. View at Publisher · View at Google Scholar · View at Scopus
  9. G. A. Leonov and N. V. Kuznetsov, “Hidden attractors in dynamical systems: from hidden oscillations in Hilbert-Kolmogorov, Aizerman, and KALman problems to hidden chaotic attractor in Chua circuits,” International Journal of Bifurcation and Chaos, vol. 23, no. 1, Article ID 1330002, 69 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. G. A. Leonov, N. V. Kuznetsov, N. A. Korzhemanova, and D. V. Kusakin, “Lyapunov dimension formula for the global attractor of the Lorenz system,” Communications in Nonlinear Science and Numerical Simulation, vol. 41, pp. 84–103, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. G. A. Leonov, N. V. Kuznetsov, and T. N. Mokaev, “Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion,” The European Physical Journal Special Topics, vol. 224, no. 8, pp. 1421–1458, 2015. View at Publisher · View at Google Scholar · View at Scopus
  12. N. V. Kuznetsov, T. N. Mokaev, and P. A. Vasilyev, “Numerical justification of Leonov conjecture on LYApunov dimension of Rossler attractor,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 4, pp. 1027–1034, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. N. V. Kuznetsov, G. A. Leonov, M. V. Yuldashev, and R. V. Yuldashev, “Hidden attractors in dynamical models of phase-locked loop circuits: limitations of simulation in MATLAB and SPICE,” Communications in Nonlinear Science and Numerical Simulation, vol. 51, pp. 39–49, 2017. View at Publisher · View at Google Scholar · View at Scopus
  14. E. M. Elsayed and A. M. Ahmed, “Dynamics of a three-dimensional systems of rational difference equations,” Mathematical Methods in the Applied Sciences, vol. 39, no. 5, pp. 1026–1038, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  15. L. Stenflo, “Generalized Lorenz equations for acoustic-gravity waves in the atmosphere,” Physica Scripta, vol. 53, no. 1, pp. 83-84, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. G. A. Leonov, “Generalized Lorenz equations for acoustic-gravity waves in the atmosphere. Attractors dimension, convergence and homoclinic trajectories,” Communications on Pure and Applied Analysis, vol. 16, no. 6, pp. 2253–2267, 2017. View at Publisher · View at Google Scholar · View at MathSciNet
  17. Y.-M. Chen and H.-H. Liang, “Zero-zero-Hopf bifurcation and ultimate bound estimation of a generalized Lorenz-Stenflo hyperchaotic system,” Mathematical Methods in the Applied Sciences, vol. 40, no. 10, pp. 3424–3432, 2017. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. 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 · View at Scopus
  19. 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 MathSciNet · View at Scopus