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Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

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Abstract

We study the emergence of oscillatory self-sustained behavior in a nonequilibrium Nambu system that features an exchange between different kinetical and potential energy forms. To this end, we study the Yamaleev oscillator in a canonical-dissipative framework. The bifurcation diagram of the nonequilibrium Yamaleev oscillator is derived and different bifurcation routes that are leading to limit cycle dynamics and involve pitchfork and Hopf bifurcations are discussed. Finally, an analytical expression for the probability density of the stochastic nonequilibrium oscillator is derived and it is shown that the shape of the density function is consistent with the oscillator properties in the deterministic case.

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References

  1. Y. Nambu, Phys. Rev. D 7, 2405 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  2. S.A. Pandit, A.D. Gangal, J. Phys. A 31, 2899 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. A.R. Plastino, A. Plastino, L.R. da Silva, M. Casas, Physica A 271, 343 (1999)

    Article  ADS  Google Scholar 

  4. G.B. Roston, A.R. Plastino, M. Casas, A. Plastino, L.R. da Silva, Eur. Phys. J. B 48, 87 (2005)

    Article  ADS  Google Scholar 

  5. W.H. Steeb, N. Euler, Nuovo Cim. B 106, 263 (1991)

    Article  MathSciNet  ADS  Google Scholar 

  6. A. Tegmen, Czech. J. Phys. 54, 749 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  7. D. Baleanu, Proc. Inst. Math. NAS of Ukraine 50, 611 (2004)

    MathSciNet  Google Scholar 

  8. T.L. Curtright, C. Zachos, New J. Phys. 4, 83.1 (2002)

    Article  MathSciNet  Google Scholar 

  9. T.L. Curtright, C. Zachos, Phys. Rev. D 68, 085001 (2002)

    Article  ADS  Google Scholar 

  10. C. Zachos, Phys. Lett. B 570, 82 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. S. Codriansky, C.A.G. Bernardo, A. Aglaee, F. Carrillo, J. Castellanos, G. Pereira, J. Perez, J. Phys. A 27, 2565 (1994)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. M. Hirayama, Phys. Rev. D 16, 530 (1977)

    Article  ADS  Google Scholar 

  13. A.R. Plastino, A. Plastino, Physica A 232, 458 (1996)

    Article  MathSciNet  ADS  Google Scholar 

  14. N.G. Pletnev, Siberian Electronic Mathematical Reports 6, 272 (2009)

    MathSciNet  Google Scholar 

  15. R.M. Yamaleev, Ann. Phys. 292, 157 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  16. T.D. Frank, J. Biol. Phys. 37, 375 (2011)

    Article  Google Scholar 

  17. T.D. Frank, Nambu brackt formulation of nonlinear biochemical reactions beyond elementary mass action kinetics, J. Nonlin. Math. Phys., in press

  18. R.M. Yamaleev, Ann. Phys. 277, 1 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  19. R.M. Yamaleev, Ann. Phys. 285, 141 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  20. C. Gonera, Y. Nuktu, Phys. Lett. A 285, 301 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A. Tegmen, A. Vercin, Int. J. Mod. Phys. B 19, 393 (2004)

    MathSciNet  ADS  MATH  Google Scholar 

  22. F. Schweitzer, Brownian agents and active particles (Springer, Berlin, 2003)

  23. H. Haken, Z. Phys. 263, 267 (1973)

    Article  MathSciNet  ADS  Google Scholar 

  24. M. Hongler, D.M. Ryter, Z. Phys. B 31, 333 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  25. W. Ebeling, I.M. Sokolov, Statistical thermodynamics and stochastic theory of nonequilibrium systems (World Scientific, Singapore, 2004)

  26. U. Erdmann, W. Ebeling, A. Mikhailov, Phys. Rev. E 71, 051904 (2005)

    Article  ADS  Google Scholar 

  27. W. Ebeling, L. Schimansky-Geier, Eur. Phys. J. Special Top. 157, 17 (2008)

    Article  ADS  Google Scholar 

  28. W. Ebeling, F. Schweitzer, B. Tilch, Bio. Syst. 49, 17 (1999)

    Google Scholar 

  29. B. Lindner, E.M. Nicola, Eur. Phys. J. Special Top. 157, 43 (2008)

    Article  ADS  Google Scholar 

  30. A. Czirok, A.L. Barabasi, T. Vicsek, Phys. Rev. Lett. 82, 209 (1999)

    Article  ADS  Google Scholar 

  31. J.W. Rayleigh, Theory of sound, 1st edn. (Dover, New York, 1945), published 1894

  32. T.D. Frank, Eur. Phys. J. B 74, 195 (2010)

    Article  ADS  Google Scholar 

  33. T.D. Frank, Phys. Lett. A 374, 3136 (2010)

    Article  ADS  Google Scholar 

  34. A. Molgado, A. Rodriguez, J. Nonlin. Math. Phys. 14, 534 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  35. H. Risken, The Fokker-Planck equation – Methods of solution and applications (Springer, Berlin, 1989)

  36. A.L. Harvey, Phys. Rev. D 6, 1474 (1972)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Faculty of Science, Department of Physics, Kasetsart University, 10900, Bangkok, Thailand

    S. Mongkolsakulvong & P. Chaikhan

  2. Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, 06269, CT, USA

    T. D. Frank

  3. Systems Biology Ireland, University College Dublin, Belfield, 4, Dublin, Ireland

    T. D. Frank

  4. UCD School of Physics, University College Dublin, Belfield, 4, Dublin, Ireland

    T. D. Frank

Authors
  1. S. Mongkolsakulvong
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  2. P. Chaikhan
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  3. T. D. Frank
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Correspondence to T. D. Frank.

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Mongkolsakulvong, S., Chaikhan, P. & Frank, T.D. Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator. Eur. Phys. J. B 85, 90 (2012). https://doi.org/10.1140/epjb/e2012-20720-4

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  • DOI: https://doi.org/10.1140/epjb/e2012-20720-4

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