ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Logunov M. J., Butkovskij O. J. Estimation of mixing velocity in chaotic systems. Izvestiya VUZ. Applied Nonlinear Dynamics, 2008, vol. 16, iss. 4, pp. 74-82. DOI: 10.18500/0869-6632-2008-16-4-74-82

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
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Language: 
Russian
Article type: 
Article
UDC: 
531.39

Estimation of mixing velocity in chaotic systems

Autors: 
Logunov Maksim Jurevich, Federal State Budget Educational Institution of Higher Professional Education "Vladimir Grigorievich Vladimir State University and Nikolai Grigorievich Stoletovykh"
Butkovskij Oleg Jaroslavovich, Federal State Budget Educational Institution of Higher Professional Education "Vladimir Grigorievich Vladimir State University and Nikolai Grigorievich Stoletovykh"
Abstract: 

In the paper an effect of phase space trajectories mixing in chaotic systems is considered. Approximate analytic estimations are given of mixing dynamics in discrete and continuous chaotic systems. Easy algorithm is developed for experimental calculation of mixing degree and mixing velocity, both local and average over the attractor. Results of this algorithm application to Henon map and to Chua system are discussed.

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Reference: 
  1. Baladi V. Decay of correlations // in Smooth Ergodic Theory and its Applications. Proc. Symp. Pure Mathematics, Providence, RI: American Mathematical Society. 1999. Vol. 69. P. 297.
  2. Collet P., Eckmann J. Liapunov multipliers and decay of correlations in dynamical systems // Journal of Statistical Physics. 2004. Vol. 115. P. 217.
  3. Wonhas A., Vassilicos J.C. Mixing in fully chaotic flows // Physical Review E. 2002. 66.
  4. Casati G., Prosen T. Mixing property of triangular billiards // Phys. Rev. Lett. 1999. Vol. 83. P. 4729.
  5. Peifer M., Schelter B., Winterhalder M. et al. Mixing properties of the Ressler system and consequences for coherence and synchronization // Physical Review E. 2005. 72.
  6. Анищенко В.С., Астахов С.В. Относительная энтропия как мера степени перемешивания зашумленных систем // Письма в ЖТФ. 2007. Т. 33, вып. 21. C. 1.
  7. Wiggins S., Ottino J.M. Foundations of chaotic mixing // Phil. Trans. R. Soc. Lond. A. 2004. Vol. 362. P. 937.
  8. Badii R., Heinzelmann K., Meier P., Politi A. Correlation function and generalized Lyapunov exponents // Phys. Rev. A. 1988. Vol. 37, 4.
  9. Кроновер Р.М. Фракталы и хаос в динамических системах. Основы теории. М.: Постмаркет, 2000. 352 с.
  10. Alves J.F., Luzzatto S., Pinheiro V. Lyapunov exponents and rates of mixing for one-dimensional maps // Ergodic Theory and Dynamical Systems. 2004. Vol. 24. P. 637.
  11. Niu X., Lee Y. Efficient spatial-temporal chaotic mixing in microchannels // J. Micromech. Microeng. 2003. Vol. 13. P. 454.
Received: 
30.10.2007
Accepted: 
31.03.2008
Published: 
31.10.2008
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