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Control effects of Morlet wavelet term on Weierstrass–Mandelbrot function model

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Abstract

In this paper, we have investigated the control problem of the Weierstrass–Mandelbrot function model with Morlet wavelet term. Based on the corollary for its convergence, we have formulated several theorems about the monotonous effects of Morlet wavelet term on scope of the series. In addition, effects of Morlet wavelet term on two important statistical characteristics: multifractality and Hurst exponent have been calculated. We have used simulation examples to illustrate the control effects.

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References

  1. B Mandelbrot Fractals: Form, Chance, and Dimension (San Francisco: Freeman) (1977)

    MATH  Google Scholar 

  2. K Falconer Fractal Geometry, Mathematical Foundations and Applications (England: Wiley) (2003)

    Book  MATH  Google Scholar 

  3. G Daccord and R Lenormand Nature 325 41 (1987)

    Article  ADS  Google Scholar 

  4. F Igor and M Vladimir Phys. Rev. E 79 061923 (2009)

    Article  MathSciNet  Google Scholar 

  5. A P Micolich et al. Phys. Rev. Lett. 87 036802 (2001)

    Article  ADS  Google Scholar 

  6. Y Sawada, A Dougherty and J P Gollub Phys. Rev. Lett. 56 1260 (1986)

    Article  ADS  Google Scholar 

  7. M C Teich and S B Lowen IEEE Eng. Med. Biol. 13 197 (1994)

    Article  Google Scholar 

  8. K J Vinoy, K A Jose, V K Varadan and V V Varadan Microw. Opt. Techn. Let. 29 215 (2001)

    Article  Google Scholar 

  9. K J Vinoy, J K Abraham and V K Varadan IEEE T. Antenn. Propag. 51 2296 (2003)

    Article  ADS  Google Scholar 

  10. C Puente-Baliarda, J Romeu, R Pous and A Cardama IEEE Trans Antennas Propag. 46 517 (1998)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  11. M V Berry and Z V Lewis Proc. R. Soc. Lond. A 379 459 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  12. S Jiang and Y Zheng P. I. Mech. Eng. C-J. Mec. 224 959 (2010)

    Article  Google Scholar 

  13. J A C Humphrey, C A Schuler and B Rubinsky Fluid Dyn. Res. 9 81 (1992)

    Google Scholar 

  14. D A Silva et al. J. Biomed. Mater. Res. A 101A 326 (2013)

    Article  Google Scholar 

  15. N Ibrahim, A Parsa, B Hassan, P van der Stelt and D WismeijerDentomaxillofac. Radiol. 42 20120075 (2013)

    Google Scholar 

  16. I Sanchez and G Uzcategui J. Dent. 39 273 (2011)

    Article  Google Scholar 

  17. L Liu, F Hu, J Li and L L Song Climatic Environ. Res. 18 43 (2013)

    Google Scholar 

  18. K Yao, Y S Liang and F Zhang Chaos Soliton. Fract. 41 2538 (2009)

    MATH  Google Scholar 

  19. P Borgnat and P Flandrin Appl. Comput. Harmon. Anal. 15 134 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  20. R Kutner and F Świtala Quant. Financ. 3 201 (2003)

    Article  Google Scholar 

  21. T Gubiec, T R Werner, R Kutner and D Sornette Eur. Phys. J. -Spec. Top. 205 27 (2012)

    Article  Google Scholar 

  22. P Liu and S T Liu Indian J. Phys. 86 455 (2012)

    Article  ADS  Google Scholar 

  23. Y P Zhang Int. J. Bifurcation Chaos 23 1350083 (2013)

    Article  ADS  Google Scholar 

  24. W H Sun and H Y Lv Appl. Math. Comput. 219 8026 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  25. Y P Zhang, W Qiao and J Sun Indian J. Phys. 87 271 (2013)

    Google Scholar 

  26. C B Singh, R Choudhary, D S Jayas and J Paliwal Food Bioprocess Tech. 3 2 (2010)

    Article  Google Scholar 

  27. W SweldensSiam J. Math. Anal. 29 511 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  28. J Y Yin, Y Q Zhu, Z P Song, G M Zhang, Y Xue and J Liu Acta Seismol. Sin. 33 663 (2011)

    Google Scholar 

  29. K Schneider and O V Vasilyev Annu. Rev. Fluid Mech. 42 473 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  30. J Lin and L S Qu J. Sound Vib. 234 135 (2000)

    Article  ADS  Google Scholar 

  31. K P Zhu, Y S Wong and G S Hong Int. J. Mech. Tool. Manu. 49 537 (2009)

    Article  Google Scholar 

  32. T Chau Gait Posture 13 102 (2001)

    Article  Google Scholar 

  33. R K Hamid, P Witold and G R Kjell Neurocomputing 93 88 (2012)

    Google Scholar 

  34. K Weierstrass Über continuirliche functionen eiens reellen arguments, die für keinen werth des letzteren einen bestimmten differentia lquotienten besitzen (Berlin: Mayer & Mueller) (1895)

    Google Scholar 

  35. J J Benedetto and G Zimmermann J. Fourier Anal. Appl. 3 505 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  36. G Nemes Arch. Math. 95 161 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  37. B B Mandelbrot, D E Passoja and A J Paullay Nature 308 721 (1984)

    Google Scholar 

  38. G X Cao, L B Xu and J Cao Physica A 391 4855 (2012)

    Google Scholar 

  39. D Grech and G Pamuła Acta Phys. Pol. A 123 529 (2013)

    Article  Google Scholar 

  40. H Wang, L Xiang and R B Pandey Physica A 39 3496 (2012)

    Google Scholar 

  41. H E Hurst, P P Black and Y M Simaika Long-Term Storage: An Experimental Study (London: Constable) (1965)

    Google Scholar 

Download references

Acknowledgments

This work is supported by the Foundation for the National Natural Science Foundation of China (No. 61273088) and development of Shandong University of Political Science and Law which is named by Fractal control of the risk of futures market (No. 2013Q07B).

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Authors and Affiliations

  1. Business School, Shandong University of Political Science and Law, Jinan, 250014, China

    L Zhang

  2. College of Control Science and Engineering, Shandong University, Jinan, 250061, China

    S T Liu

  3. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, IL, 60607-7045, USA

    C Yu

Authors
  1. L Zhang
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  2. S T Liu
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  3. C Yu
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Correspondence to L Zhang.

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Zhang, L., Liu, S.T. & Yu, C. Control effects of Morlet wavelet term on Weierstrass–Mandelbrot function model. Indian J Phys 88, 867–874 (2014). https://doi.org/10.1007/s12648-014-0497-3

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  • DOI: https://doi.org/10.1007/s12648-014-0497-3

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