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Hyperchaos and quasiperiodicity from a four-dimensional system based on the Lorenz system

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Abstract

This paper reports on numerically computed parameter plane plots for a dynamical system modeled by a set of five-parameter, four autonomous first-order nonlinear ordinary differential equations. The dynamical behavior of each point, in each parameter plane, is characterized by Lyapunov exponents spectra. Each of these diagrams indicates parameter values for which hyperchaos, chaos, quasiperiodicity, and periodicity may be found. In fact, each diagram shows delimited regions where each of these behaviors happens. Moreover, it is shown that some of these parameter planes display organized periodic structures embedded in quasiperiodic and chaotic regions.

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References

  1. E. Lorenz, J. Atmos. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  2. C. Sparrow, The Lorenz equations: bifurcations, chaos, and strange attractors (Springer-Verlag, New York, 1982)

  3. A. Zarei, S. Tavakoli, Appl. Math. Comput. 291, 323 (2016)

    MathSciNet  Google Scholar 

  4. S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos (Springer, New York, 2003)

  5. M.J. Correia, P.C. Rech, Appl. Math. Comput. 218, 6711 (2012)

    MathSciNet  Google Scholar 

  6. H.G. Schuster, W. Just, Deterministic chaos an introduction (Wiley-VCH, Weinheim, 2005)

  7. F. Doveil, A. Macor, Y. Elskens, Chaos 16, 033103 (2006)

    Article  ADS  Google Scholar 

  8. F.G. Prants, P.C. Rech, Math. Comput. Simul. 136, 132 (2017)

    Article  Google Scholar 

  9. H.A. Albuquerque, R.M. Rubinger, P.C. Rech, Phys. Lett. A 372, 4793 (2008)

    Article  ADS  Google Scholar 

  10. C. Bonatto, J.A.C. Gallas, Phys. Rev. E 75, 055204 (2007)

    Article  ADS  Google Scholar 

  11. T.S. Krüger, P.C. Rech, Eur. Phys. J. D 66, 12 (2012)

    Article  ADS  Google Scholar 

  12. F.G. Prants, P.C. Rech, Eur. Phys. J. B 87, 196 (2014)

    Article  ADS  Google Scholar 

  13. P.C. Rech, Int. J. Bifurc. Chaos 25, 1530035 (2015)

    Article  MathSciNet  Google Scholar 

  14. P.C. Rech, Phys. Scr. 91, 075201 (2016)

    Article  ADS  Google Scholar 

Download references

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Authors and Affiliations

  1. Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710, Joinville, Brazil

    Paulo C. Rech

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  1. Paulo C. Rech
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Correspondence to Paulo C. Rech.

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Rech, P.C. Hyperchaos and quasiperiodicity from a four-dimensional system based on the Lorenz system. Eur. Phys. J. B 90, 251 (2017). https://doi.org/10.1140/epjb/e2017-80533-5

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  • DOI: https://doi.org/10.1140/epjb/e2017-80533-5

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