Skip to main content
Log in

Numerical and physical modeling of the dynamics of the Lorenz system

  • Published:
Numerical Analysis and Applications Aims and scope Submit manuscript

Abstract

This paper describes a modification of the method of power series for the construction of approximate solutions of the Lorenz system. The results of a computer-aided simulation are presented. Also, physical modeling of the dynamics of the Lorenz system for processes occurring in an electric circuit is considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Lorenz, E., Deterministic Nonperiodic Flow, J. Atmos. Sci., 1963, vol. 20, no. 2, pp. 130–141.

    Article  Google Scholar 

  2. Landa, P.C., Nelineinye kolebaniya i volny (Nonlinear Oscillations and Waves), Moscow: LIBROKOM, 2010.

    Google Scholar 

  3. Pokrovskii, L.A., Solving the System of Lorenz Equations in the Asymptotic Limit of a Large Rayleigh Number. I. The Lorenz System in the Simplest Quantum Laser Model under Application of the Averaging Method, Teor. Mat. Fiz., 1985, vol. 62, no. 2, pp. 272–290.

    Article  MathSciNet  Google Scholar 

  4. Neumark, Yu.I. and Landa, O.S., Stokhasticheskie i khaoticheskie kolebaniya (Stochastic and Chaotic Oscillations), Moscow: LIBROKOM, 2009.

    Google Scholar 

  5. Nemytskii, V.V. and Stepanov, V.V., Kachestvennaya teoriya differentsialnykh uravnenii (Qualitative Theory of Differential Equations), Moscow: Editorial URSS, 2004.

    Google Scholar 

  6. Yorke, J. and Yorke, E., Metastable Chaos: The Transition to Sustained Chaotic Behavior in the Lorenz Model, J. Stat. Phys., 1979, vol. 21, no. 3, pp. 263–278.

    Article  MathSciNet  Google Scholar 

  7. Sparrow, C., The Lorenz Equations: Bifurcation, Chaos, and Strange Attractors, New York: Springer-Verlag, 1982.

    Book  Google Scholar 

  8. Kaloshin, D.A., Search for and Stabilization of Unstable Saddle Cycles in the Lorenz System, Diff. Eq., 2001, vol. 37, no. 11, pp. 1636–1639.

    Article  MATH  MathSciNet  Google Scholar 

  9. Magnitskii, N.A. and Sidorov, S.V., Novye metody khaoticheskoi dinamiki (New Methods of Chaotic Dynamics), Moscow: Editorial URSS, 2004.

    Google Scholar 

  10. Babuska, I., Vitasek, E., and Prager, M., Chislennye protsessy resheniya differentsialnykh uravnenii (Numerical Processes in Differential Equations), Moscow: Mir, 1969.

    Google Scholar 

  11. The MPFR Library for Multiple-Precision Floating-Point Computations with Correct Rounding; http:www.mpfr.org/.

  12. Dmitriev, A.S. and Panas, A.I., Dimanicheskii khaos: novye nositeli informatsii dlya sistem svyazi (Dynamic Chaos: New Information Carriers for Communication Systems), Moscow: Fizmatlit, 2002.

    Google Scholar 

  13. Texas Instruments Incorporated [SBFS017A].MPY634:Wide Bandwidth Precision Analog Multiplier (Data Sheet); http:www.ti.com/lit/ds/symlink/mpy634.pdf, 2011.

  14. Matveev, N.M., Metody integrirovaniya obyknovennykh differentsialnykh uravnenii (Methods of Integration of Ordinary Differential Equations), Moscow: Vysschaya Shkola, 1967.

    Google Scholar 

  15. Bakhvalov, N.S., Zhidkov, N.P., and Kobel’kov, G.M., Chislennye metody ( Numerical Methods), Moscow: BINOM, Laboratoriya Znanii, 2011.

    Google Scholar 

  16. Fichtengoltz, G.M., Kurs differentsialnogo i integralnogo ischisleniya (A Course of Differential and Integral Calculus), vol. 2, Moscow: Nauka, 1966.

    Google Scholar 

  17. Pchelintsev, A.N., On Constructing Generally Periodic Solutions of a Complicated Structure of a Non-Autonomous System of Differential Equations, Sib. Zh. Vych. Mat., 2013, vol. 16, no. 1, pp. 63–71.

    MATH  MathSciNet  Google Scholar 

  18. Tucker W., A Rigorous ODE Solver and Smale’s 14th Problem, Found. Comput. Math., 2002, vol. 2, no. 1, pp. 53–117.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. N. Pchelintsev.

Additional information

Original Russian Text © A.N. Pchelintsev, 2014, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2014, Vol. 17, No. 2, pp. 191–201.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pchelintsev, A.N. Numerical and physical modeling of the dynamics of the Lorenz system. Numer. Analys. Appl. 7, 159–167 (2014). https://doi.org/10.1134/S1995423914020098

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1995423914020098

Keywords

Navigation