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Dynamical and fractal properties in periodically forced stretch-twist-fold (STF) flow

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Abstract.

The periodically forced stretch-twist-fold (STF) flow is introduced in this article. The nonlinear behavior of the STF flow with periodic force along the y -axis is investigated analytically and numerically. The STF flow is a prototype of the dynamo theory that proposes a mechanism of magnetic field generation continuously. The stability analysis is done by Routh Huwritz criteria and Cardano method. Chasing chaos through numerical simulation is determined to demonstrate the chaotic behavior of the forced STF flow. With the help of fractal processes based on the forced STF flow, a multi-wing forced STF flow is obtained that gives a n -wing forced STF flow system.

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References

  1. J. Lu, G. Chen, S. Zhang, Chaos, Solitons Fractals 14, 669 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  2. Mauro Bologna, Eur. Phys. J. Plus 131, 386 (2016)

    Article  Google Scholar 

  3. Q. Gao, J. Ma, Nonlinear Dyn. 58, 209 (2009)

    Article  Google Scholar 

  4. M. Aqeel, S. Ahmad, Nonlinear Dyn. 84, 755 (2015)

    Article  Google Scholar 

  5. S.H. Strogatz, Nonlinear Dynamics and Chaos: With Application to Physics, Biology, Chemistry, and Engineering (Westview, New York, 2000)

  6. S.T. Kingni, S. Jafari, H. Simo, P. Woafo, Eur. Phys. J. Plus 129, 76 (2014)

    Article  Google Scholar 

  7. E.N. Lorenz, J. At. Sci. 20, 130 (1963)

    Article  ADS  Google Scholar 

  8. O.E. Rossler, Phys. Lett. A 57, 397 (1976)

    Article  ADS  Google Scholar 

  9. J.C. Sprott, Phys. Rev. E 50, 647 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  10. G.R. Chen, T. Ueta, Int. J. Bifurcat. Chaos 9, 1465 (1999)

    Article  Google Scholar 

  11. K. Bajer, H.K. Moffatt, J. Fluid Mech. 212, 337 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  12. E.N. Lorenz, Tellus 43, 505 (1982)

    ADS  Google Scholar 

  13. T.N. Palmer, J. Clim. 12, 575 (1999)

    Article  ADS  Google Scholar 

  14. S. Corti, F. Molteni, T.N. Palmer, Nature 398, 799 (1999)

    Article  ADS  Google Scholar 

  15. A.K. Mittal, S. Dwivedi, A.C. Panedy, Ind. J. Radio Space Phys. 32, 209 (2003)

    Google Scholar 

  16. Dibakar Ghosh, R. Anirban, A.R. Chowdhury, J. Comput. Nonlinear Dyn. 5, 1 (2010)

    Google Scholar 

  17. K.M. Ashok, M. Sandipan, P.S. Ravi, Commun. Nonlinear Sci. Numer. Simulat. 16, 787 (2011)

    Article  Google Scholar 

  18. S. Khatiwala, B.E. Shaw, M.A. Cane, Geophys. Res. Lett. 28, 2633 (2001)

    Article  ADS  Google Scholar 

  19. H. Debin, Prog. Theor. Phys. 112, 785 (2004)

    Article  Google Scholar 

  20. G.L. Feng, W.P. He, Chin. Phys. 16, 2825 (2007)

    Article  ADS  Google Scholar 

  21. S.I. Vainshtein, Y.A.B. Zel'dovich, Sov. Phys. Usp. 15, 159 (1972)

    Article  ADS  Google Scholar 

  22. H.K. Moffatt, M.R.E. Proctor, J. Fluid Mech. 154, 493 (1985)

    Article  ADS  Google Scholar 

  23. K. Bajer, H.K. Moffatt, F.H. Nex, In. H.K. Moffatt, Topological Fluid Mechanics, Proceedings of the IUTAM Symposium, edited by A. Tsinober (Cambridge University Press, Cambridge, 1990)

  24. T. Zhou, Y. Tang, G. Chen, Int. J. Bifurcat. Chaos 9, 3167 (2001)

    Google Scholar 

  25. Christopher P. Silva, IEEE Trans. Circuits Syst. I. Fundam. Theory 40, 675 (1993)

    Article  Google Scholar 

  26. Z. Zheng, G. Chen, J. Math Anal. Appl. 315, 106 (2006)

    Article  MathSciNet  Google Scholar 

  27. R. Miranda, Phys. Lett. A 178, 105 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  28. R.L. Borrelli, C.S. Coleman, Differential Equations, fourth edition (John Wiley and Sons, Inc., New York, 1998)

  29. W.E. Boyce, R.C. Diprima, Elementary Differential Equations and Boundary Value Problems, eight edition (John Wiley and Sons, Inc., United States of America, 2010)

  30. R. Zhang, G. Sun, The Second International Conference on Intelligent Control and Information Processing (ICICIP), Vol. 1 (IEEE, 2011) p. 177

  31. J. Mikolajski, E. Schmeidel, Opuscula Math. 26, 343 (2006)

    MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Applied Mathematics & Statistics, Institute of Space Technology, Islamabad, Pakistan

    Muhammad Aqeel, Salman Ahmad, Anam Azam & Faizan Ahmed

Authors
  1. Muhammad Aqeel
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  2. Salman Ahmad
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  3. Anam Azam
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  4. Faizan Ahmed
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Correspondence to Muhammad Aqeel.

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Aqeel, M., Ahmad, S., Azam, A. et al. Dynamical and fractal properties in periodically forced stretch-twist-fold (STF) flow. Eur. Phys. J. Plus 132, 219 (2017). https://doi.org/10.1140/epjp/i2017-11487-7

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