The European Physical Journal Special Topics

, Volume 224, Issue 8, pp 1469–1476 | Cite as

Recent new examples of hidden attractors

  • S. Jafari
  • J. C. Sprott
  • F. Nazarimehr
Part of the following topical collections:
  1. Multistability: Uncovering Hidden Attractors


Hidden attractors represent a new interesting topic in the chaos literature. These attractors have a basin of attraction that does not intersect with small neighborhoods of any equilibrium points. Oscillations in dynamical systems can be easily localized numerically if initial conditions from its open neighborhood lead to a long-time oscillation. This paper reviews several types of new rare chaotic flows with hidden attractors. These flows are divided into to three main groups: rare flows with no equilibrium, rare flows with a line of equilibrium points, and rare flows with a stable equilibrium. In addition we describe a novel system containing hidden attractors.


Equilibrium Point Lyapunov Exponent Chaotic System European Physical Journal Special Topic Stable Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. 1.
    N. Kuznetsov, G. Leonov, S. Seledzhi, IFAC Proc. Vol. (IFAC-PapersOnline) 18, 2506 (2011)Google Scholar
  2. 2.
    N. Kuznetsov, G. Leonov, V. Vagaitsev, IFAC Proc. Vol. (IFAC-PapersOnline) 4, 29 (2010)Google Scholar
  3. 3.
    G. Leonov, N. Kuznetsov, Dokl. Math. 84, 475 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    G. Leonov, N. Kuznetsov, IFAC Proc. Vol. (IFAC-PapersOnline) 18, 2494 (2011)Google Scholar
  5. 5.
    G. Leonov, N. Kuznetsov, J. Math. Sci. 201, 645 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    G. Leonov, N. Kuznetsov, M. Kiseleva, E. Solovyeva, A. Zaretskiy, Nonlinear Dyn. 77, 277 (2014)CrossRefzbMATHGoogle Scholar
  7. 7.
    G. Leonov, N. Kuznetsov, V. Vagaitsev, Phys. Lett. A 375, 2230 (2011)MathSciNetADSCrossRefzbMATHGoogle Scholar
  8. 8.
    G. Leonov, N. Kuznetsov, V. Vagaitsev, Phys. D: Nonlinear Phenomena 241, 1482 (2012)MathSciNetADSCrossRefzbMATHGoogle Scholar
  9. 9.
    G. Leonov, N. Kuznetsov, Numerical Methods for Differential Equations, Optimization, and Technological Problems, 41 (2013)Google Scholar
  10. 10.
    G. Leonov, N. Kuznetsov, Int. J. Bifurc. Chaos 23 (2013)Google Scholar
  11. 11.
    V. Bragin, V. Vagaitsev, N. Kuznetsov, G. Leonov, J. Comput. Syst. Sci. Int. 50, 511 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    E.N. Lorenz, J. Atmos. Sci. 20, 130 (1963)ADSCrossRefGoogle Scholar
  13. 13.
    O.E. Rossler, Phys. Lett. A 57, 397 (1976)ADSCrossRefGoogle Scholar
  14. 14.
    G. Chen, T. Ueta, Int. J. Bifurc. Chaos 9, 1465 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    J. Sprott, Phys. Rev. E 50, R647 (1994)MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    X. Wang, G. Chen, Comm. Nonlin. Sci. Numer. Simul. 17, 1264 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    Z. Wei, Phys. Lett. A 376, 102 (2011)MathSciNetADSCrossRefzbMATHGoogle Scholar
  18. 18.
    S. Jafari, J. Sprott, S.M.R.H. Golpayegani, Phys. Lett. A 377, 699 (2013)MathSciNetADSCrossRefGoogle Scholar
  19. 19.
    M. Molaie, S. Jafari, J.C. Sprott, S.M.R.H. Golpayegani, Int. J. Bifurc. Chaos 23 (2013)Google Scholar
  20. 20.
    S. Jafari, J. Sprott, Chaos, Solitons Fractals 57, 79 (2013)MathSciNetADSCrossRefGoogle Scholar
  21. 21.
    W.G. Hoover, Phys. Rev. E 51 (1995)Google Scholar
  22. 22.
    H.A. Posch, W.G. Hoover, F.J. Vesely, Phys. Rev. A 33, 4253 (1986)MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    D. Cafagna, G. Grassi, Math. Prob. Eng. (2013)Google Scholar
  24. 24.
    D. Cafagna, G. Grassi, Commun. Nonlinear Sci. Numer. Simul. 19, 2919 (2014)MathSciNetADSCrossRefGoogle Scholar
  25. 25.
    U. Chaudhuri, A. Prasad, Phys. Lett. A 378, 713 (2014)MathSciNetADSCrossRefGoogle Scholar
  26. 26.
    A. Kuznetsov, S. Kuznetsov, E. Mosekilde, N. Stankevich, J. Phys. A: Math. Theor. 48, 125101 (2015)MathSciNetADSCrossRefGoogle Scholar
  27. 27.
    V.-T. Pham, S. Jafari, C. Volos, X. Wang, S.M.R.H. Golpayegani, Int. J. Bifurc. Chaos 24 (2014)Google Scholar
  28. 28.
    V.-T. Pham, F. Rahma, M. Frasca, L. Fortuna, Int. J. Bifurc. Chaos 24 (2014)Google Scholar
  29. 29.
    V.-T. Pham, C. Volos, S. Jafari, Z. Wei, X. Wang, Int. J. Bifurc. Chaos 24 (2014)Google Scholar
  30. 30.
    A. Prasad, [arXiv preprint] [arXiv:1409.4921] (2014)
  31. 31.
    X. Wang, G. Chen, Nonlinear Dyn. 71, 429 (2013)CrossRefGoogle Scholar
  32. 32.
    S. Huan, Q. Li, X.-S. Yang, Int. J. Bifurc. Chaos 23 (2013)Google Scholar
  33. 33.
    S. Jafari, J.C. Sprott, V.-T. Pham, S.M.R.H. Golpayegani, A.H. Jafari, Int. J. Bifurc. Chaos 24 (2014)Google Scholar
  34. 34.
    S. Kingni, S. Jafari, H. Simo, P. Woafo, Eur. Phys. J. Plus 129, 1 (2014)CrossRefGoogle Scholar
  35. 35.
    S.-K. Lao, Y. Shekofteh, S. Jafari, J.C. Sprott, Int. J. Bifurc. Chaos 24 (2014)Google Scholar
  36. 36.
    S. Vaidyanathan, Computational Intelligence and Computing Research (ICCIC), 2012 IEEE International Conference (2012), p. 1Google Scholar
  37. 37.
    X. Wang, G. Chen, Proceedings of the 2011 Fourth International Workshop on Chaos-Fractals Theories and Applications 2011, 82 (2011)Google Scholar
  38. 38.
    Z. Wei, R. Wang, A. Liu, Math. Comput. Simul. 100, 13 (2014)MathSciNetCrossRefGoogle Scholar
  39. 39.
    Z. Wei, W. Zhang, Int. J. Bifurc. Chaos 24 (2014)Google Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.Biomedical Engineering DepartmentAmirkabir University of TechnologyTehranIran
  2. 2.Department of PhysicsUniversity of WisconsinMadisonUSA

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