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Nonlinear Dynamics

, Volume 84, Issue 1, pp 311–322 | Cite as

Optimal nonlinear dynamics modeling method for big data based on fractional calculus and simulated annealing

  • Dingju Zhu
Original Paper

Abstract

No nonlinear dynamics modeling method for big data has been proposed, and no nonlinear dynamics modeling method based on fractional calculus and simulated annealing has been proposed until now. This paper provided the optimal nonlinear dynamics modeling method for big data based on fractional calculus and simulated annealing, which can find the optimal nonlinear dynamics model for big data based on fractional-order calculus. This paper also provided another alternative method that the nonlinear dynamics modeling method for big data is based on integer-order calculus. This paper took price, supply–demand ratio and selling rate big data as an application to illustrate the proposed methods. And this paper compared the optimal nonlinear dynamics modeling method for big data based on fractional calculus and simulated annealing with the alternative method based on integer-order calculus, and concluded that the nonlinear dynamics model found by the method based on fractional calculus and simulated annealing is closer to the real system than the nonlinear dynamics model found by the method based on integer-order calculus.

Keywords

Nonlinear dynamics model Big data Fractional calculus Simulated annealing 

Notes

Acknowledgments

This research was supported by University-industry Collaborative Innovation Transfer and Transformation Project of Guangdong Province under Grant No. 2014B090901064 and Major Project of National Social Science Fund under Grant No. 14ZDB101, National Natural Science Foundation of China under Grant No. 61105133.

References

  1. 1.
    Chen, W.C.: Nonlinear dynamics and chaos in a fractional-order financial system. Chaos Solitons Fractals 36(5), 1305–1314 (2008)CrossRefGoogle Scholar
  2. 2.
    Magin, R.L.: Fractional calculus models of complex dynamics in biological tissues. Comput. Math. Appl. 59(5), 1586–1593 (2010)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Li, Y., Chen, Y.Q., Podlubny, I.: Mittag–Leffler stability of fractional order nonlinear dynamic systems. Automatica 45(8), 1965–1969 (2009)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    West, B.J.: Colloquium: fractional calculus view of complexity: a tutorial. Rev. Mod. Phys. 86(4), 1169 (2014)CrossRefGoogle Scholar
  5. 5.
    Machado, J.T., Mainardi, F., Kiryakova, V.: Fractional calculus: quo vadimus? (Where are we Going?). Fract. Calc. Appl. Anal. 18(2), 495–526 (2015)MathSciNetMATHGoogle Scholar
  6. 6.
    Sabzikar, F., Meerschaert, M.M., Chen, J.: Tempered fractional calculus. J. Comput. Phys. 293, 14–28 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Machado, J.A.T., Galhano, A.M.S.F., Trujillo, J.J.: On development of fractional calculus during the last fifty years. Scientometrics 98(1), 577–582 (2014)Google Scholar
  8. 8.
    Almeida, R., Torres, D.F.M.S.: Computational Methods in the Fractional Calculus of Variations. Imperial College Press, London (2015)CrossRefMATHGoogle Scholar
  9. 9.
    Marz, N., Warren, J.: Big Data: Principles and Best Practices of Scalable Realtime Data Systems. Manning Publications Co., Greenwich (2015)Google Scholar
  10. 10.
    Fox, P., Hendler, J.: The science of data science. Big Data 2(2), 68–70 (2014)CrossRefGoogle Scholar
  11. 11.
    George, G., Haas, M.R., Pentland, A.: Big data and management. Acad. Manag. J. 57(2), 321–326 (2014)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Computer ScienceSouth China Normal UniversityGuangzhouChina

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