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Hyperchaos in convection with the Cattaneo-Christov heat-flux model

  • Caio C. Daumann
  • Paulo C. RechEmail author
Regular Article
  • 15 Downloads

Abstract

In this paper, we report on the nonlinear dynamics of a five-variable, four-parameter system, which models the effects of thermal relaxation time on Rayleigh-Bénard convection of Boussinesq fluid layer heated underneath. Six cross-sections of the four-dimensional parameter-space are considered. By using Lyapunov exponents spectra to characterize the dynamical behavior at each point of each these diagrams, we show that different parameter regions are allowed, from equilibrium points to chaos and hyperchaos regions.

Graphical abstract

Keywords

Statistical and Nonlinear Physics 

References

  1. 1.
    G.C. Layek, N.C. Pati, Phys. Lett. A 381, 3568 (2017) ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    J.P. Goedgebuer, P. Levy, L. Larger, C.C. Chen, W.T. Rhodes, IEEE J. Quantum Elect. 38, 1178 (2002) ADSCrossRefGoogle Scholar
  3. 3.
    C.D. Li, X.F. Liao, K.W. Wong, Chaos Solitons Fractals 23, 183 (2005) ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    C. Gangadhar, R. Deergha, Int. J. Bifurc. Chaos 19, 3833 (2009) CrossRefGoogle Scholar
  5. 5.
    Y. Li, W.K.S. Tang, G. Chen, Int. J. Bifurc. Chaos 15, 3367 (2005) CrossRefGoogle Scholar
  6. 6.
    C. Zhu, Appl. Math. Comput. 216, 3126 (2010) Google Scholar
  7. 7.
    K. Sun, X. Liu, C. Zhu, J.C. Sprott, Nonlinear Dyn. 69, 1383 (2012) CrossRefGoogle Scholar
  8. 8.
    H. Yu, G. Cai, Y. Li, Nonlinear Dyn. 67, 2171 (2012) CrossRefGoogle Scholar
  9. 9.
    S.H. Zhang, K. Shen, Chin. Phys. 12, 149 (2003) ADSCrossRefGoogle Scholar
  10. 10.
    H. Li, X. Liao, C. Li, C. Li, Neurocomputing 74, 3212 (2011) CrossRefGoogle Scholar
  11. 11.
    H. Li, X. Liao, M. Luo, Nonlinear Dyn. 68, 137 (2012) CrossRefGoogle Scholar
  12. 12.
    Z. Yan, P. Yu, Int. J. Bifurc. Chaos 17, 1759 (2007) CrossRefGoogle Scholar
  13. 13.
    G. Vidal, H. Mancini, Int. J. Bifurc. Chaos 20, 885 (2010) CrossRefGoogle Scholar
  14. 14.
    A.N. Njah, Nonlinear Dyn. 61, 1 (2010) MathSciNetCrossRefGoogle Scholar
  15. 15.
    D. Cafagna, G. Grassi, Nonlinear Dyn. 68, 117 (2012) CrossRefGoogle Scholar
  16. 16.
    Z. Sun, G. Si, F. Min, Y. Zhang, Nonlinear Dyn. 68, 471 (2012) CrossRefGoogle Scholar
  17. 17.
    S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer, New York, 2003) Google Scholar
  18. 18.
    M.J. Correia, P.C. Rech, Appl. Math. Comput. 218, 6711 (2012) MathSciNetGoogle Scholar

Copyright information

© EDP Sciences / Società Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Departamento de Física, Universidade do Estado de Santa CatarinaJoinvilleBrazil

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