Table of Contents Author Guidelines Submit a Manuscript
Advances in Mathematical Physics
Volume 2016 (2016), Article ID 3142068, 6 pages
http://dx.doi.org/10.1155/2016/3142068
Research Article

A New No-Equilibrium Chaotic System and Its Topological Horseshoe Chaos

1Department of Information Engineering, Binzhou University, Binzhou 256600, China
2Department of Electrical Engineering, Binzhou University, Binzhou 256600, China
3College of Aeronautical Engineering, Binzhou University, Binzhou 256600, China
4Department of Product Design, Tianjin University of Science and Technology, Tianjin 300457, China
5School of Electrical Engineering and Automation, Tianjin University, Tianjin 300072, China

Received 13 September 2016; Revised 11 November 2016; Accepted 6 December 2016

Academic Editor: Xavier Leoncini

Copyright © 2016 Chunmei Wang 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. Chen and T. Ueta, “Yet another chaotic attractor,” International Journal of Bifurcation and Chaos, vol. 9, no. 7, pp. 1465–1466, 1999. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  3. W. Zhang and W. L. Hao, “Multi-pulse chaotic dynamics of six-dimensional non-autonomous nonlinear system for a composite laminated piezoelectric rectangular plate,” Nonlinear Dynamics, vol. 73, no. 1-2, pp. 1005–1033, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  4. S. Cang, A. Wu, Z. Wang, W. Xue, and Z. Chen, “Birth of one-to-four-wing chaotic attractors in a class of simplest three-dimensional continuous memristive systems,” Nonlinear Dynamics, vol. 83, no. 4, pp. 1987–2001, 2016. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  5. N. Lazaryan and H. Sedaghat, “Periodic and chaotic orbits of a discrete rational system,” Discrete Dynamics in Nature and Society, vol. 2015, Article ID 519598, 8 pages, 2015. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. D. Arroyo, G. Alvarez, S. Li, C. Li, and J. Nunez, “Cryptanalysis of a discrete-time synchronous chaotic encryption system,” Physics Letters A, vol. 372, no. 7, pp. 1034–1039, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. S. Cang, Z. Wang, Z. Chen, and H. Jia, “Analytical and numerical investigation of a new Lorenz-like chaotic attractor with compound structures,” Nonlinear Dynamics, vol. 75, no. 4, pp. 745–760, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  8. S. Cang, Z. Chen, Z. Wang, and H. Jia, “Projective synchronisation of fractional-order memristive systems with different structures based on active control method,” International Journal of Sensor Networks, vol. 14, no. 2, pp. 102–108, 2013. View at Publisher · View at Google Scholar · View at Scopus
  9. D. Dudkowski, S. Jafari, T. Kapitaniak, N. V. Kuznetsov, G. A. Leonov, and A. Prasad, “Hidden attractors in dynamical systems,” Physics Reports-Review Section of Physics Letters, vol. 637, pp. 1–50, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  10. 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 in Applied Sciences and Engineering, vol. 23, no. 1, Article ID 1330002, 69 pages, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  11. G. A. Leonov, N. V. Kuznetsov, and V. I. Vagaitsev, “Localization of hidden Chua's attractors,” Physics Letters A, vol. 375, no. 23, pp. 2230–2233, 2011. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. M. Khan, T. Shah, and M. A. Gondal, “An efficient technique for the construction of substitution box with chaotic partial differential equation,” Nonlinear Dynamics, vol. 73, no. 3, pp. 1795–1801, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  13. M. P. Pettersson, G. Iaccarino, and J. Nordstrom, Polynomial Chaos Methods for Hyperbolic Partial Differential Equations, Mathematical Engineering, Springer, 2015. View at Publisher · View at Google Scholar
  14. Y. Zhang, D. Xiao, Y. Shu, and J. Li, “A novel image encryption scheme based on a linear hyperbolic chaotic system of partial differential equations,” Signal Processing: Image Communication, vol. 28, no. 3, pp. 292–300, 2013. View at Publisher · View at Google Scholar · View at Scopus
  15. 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 Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. L. Zhou and F. Chen, “Sil'nikov chaos of the Liu system,” Chaos, vol. 18, no. 1, Article ID 013113, 2008. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  17. T. Zhou, G. Chen, and S. Čelikovský, “Ši'lnikov chaos in the generalized Lorenz canonical form of dynamical systems,” Nonlinear Dynamics, vol. 39, no. 4, pp. 319–334, 2005. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. W. Xu, J. Feng, and H. Rong, “Melnikov's method for a general nonlinear vibro-impact oscillator,” Nonlinear Analysis, Theory, Methods & Applications, vol. 71, no. 1-2, pp. 418–426, 2009. View at Publisher · View at Google Scholar · View at Scopus
  19. G. Cian, “Some remarks on topological horseshoes and applications,” Nonlinear Analysis: Real World Applications, vol. 16, pp. 74–89, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  20. Q. Li and X.-S. Yang, “A simple method for finding topological horseshoes,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 20, no. 2, pp. 467–478, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  21. X.-S. Yang, “Topological horseshoes and computer assisted verification of chaotic dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, vol. 19, no. 4, pp. 1127–1145, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. X.-S. Yang and Y. Tang, “Horseshoes in piecewise continuous maps,” Chaos, Solitons & Fractals, vol. 19, no. 4, pp. 841–845, 2004. View at Publisher · View at Google Scholar · View at Scopus
  23. Q. Li and X.-S. Yang, “Chaotic dynamics in a class of three dimensional Glass networks,” Chaos, vol. 16, no. 3, Article ID 033101, 2006. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  24. V. Pham, S. Vaidyanathan, C. Volos, S. Jafari, N. Kuznetsov, and T. Hoang, “A novel memristive time–delay chaotic system without equilibrium points,” The European Physical Journal Special Topics, vol. 225, no. 1, pp. 127–136, 2016. View at Publisher · View at Google Scholar
  25. A. Akgul, H. Calgan, I. Koyuncu, I. Pehlivan, and A. Istanbullu, “Chaos-based engineering applications with a 3D chaotic system without equilibrium points,” Nonlinear Dynamics, vol. 84, no. 2, pp. 481–495, 2016. View at Publisher · View at Google Scholar · View at MathSciNet
  26. D. Cafagna and G. Grassi, “Chaos in a new fractional-order system without equilibrium points,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, no. 9, pp. 2919–2927, 2014. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  27. Z. Wang, S. Cang, E. O. Ochola, and Y. Sun, “A hyperchaotic system without equilibrium,” Nonlinear Dynamics, vol. 69, no. 1-2, pp. 531–537, 2012. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus