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Information resonance in a model excitable system

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Abstract

We consider a simple mesoscopic model of an excitable thermochemical system for which the system temperature as a function of time has a form of irregular spikes. The interspike intervals are mapped onto elements of a formal alphabet. The time evolution of system temperature is represented by a string over this alphabet. We demonstrate that the entropy of such string reaches a minimum for the values of model parameters where the coherence resonance of interspike intervals is observed.

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References

  1. G. Nicolis, I. Prigogine, Self-Organization in Nonequilibrium Systems (Wiley, New York, 1977)

  2. C.W. Gardiner, Handbook of Stochastic Methods (Springer, Berlin, 2004)

  3. N.G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland Pub., Amsterdam, 1992)

  4. L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Eur. Phys. J. B 69, 1 (2009)

    Article  ADS  Google Scholar 

  5. P. Hänggi, F. Marchesoni, Rev. Mod. Phys. 81, 387 (2009)

    Article  ADS  Google Scholar 

  6. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  7. D. Alcor, V. Croquette, L. Jullien, A. Lemarchand, Proc. Natl. Acad. Sci. USA 101, 8276 (2004)

    Article  ADS  Google Scholar 

  8. M. Yoshimoto, H. Shirahama, S. Kurosawa, J. Chem. Phys. 129, 014508 (2008)

    Article  ADS  Google Scholar 

  9. B.K. Goswami, S. Euzzor, K. Al Naimee, A. Geltrude, R. Meucci, F.T. Arecchi, Phys. Rev. E 80, 016211 (2009)

    Article  ADS  Google Scholar 

  10. J. Escorcia-Garcia, V. Agarwal, P. Parmananda, Appl. Phys. Lett. 94, 133103 (2009)

    Article  ADS  Google Scholar 

  11. A.A. Faisal, L.P. Selen, D.M. Wolpert, Nat. Rev. Neurosci. 9, 292 (2008)

    Article  Google Scholar 

  12. J.M. Smith, D.P. Bradley, M.F. James, C.L.H. Huang, Biol. Rev. Cambridge Philos. Soc. 81, 457 (2006)

    Article  Google Scholar 

  13. B. Lindner, J. Garcia-Ojalvo, A. Neiman, L. Schimansky-Geier, Phys. Rep. 392, 321 (2004)

    Article  ADS  Google Scholar 

  14. C.S. Zhou, J. Kurths, New J. Phys. 7, 18 (2005)

    Article  Google Scholar 

  15. F. Sagues, J.M. Sancho, J. Garcia-Ojalvo, Rev. Mod. Phys. 79, 829 (2007)

    Article  ADS  Google Scholar 

  16. G. Schmid, I. Goychuk, P. Hänggi, Europhys. Lett. 56, 22 (2001)

    Article  ADS  Google Scholar 

  17. P. Jung, J.W. Shuai, Europhys. Lett. 56, 29 (2001)

    Article  ADS  Google Scholar 

  18. A. Förster, M. Merget, F.W. Schneider, J. Phys. Chem. 100, 4442 (1996)

    Article  Google Scholar 

  19. W. Hohmann, J. Müller, F.W. Schneider, J. Phys. Chem. 100, 5388 (1996)

    Article  Google Scholar 

  20. S. Kadar, J. Wang, K. Showalter, Nature 391, 770 (1998)

    Article  ADS  Google Scholar 

  21. B. Nowakowski, A.L. Kawczynski, A. Kolbus, A. Lemarchand, Eur. Phys. J. B 84, 137 (2011)

    Article  ADS  Google Scholar 

  22. T. Gramss, S. Bornholdt, M. Gross, M. Mitchell, T. Pellizzari, Non-Standard Computation (Wiley-VCH, Weinhaim, 1998)

  23. A. Adamatzky, B. De Lacy Costello, T. Asai, Reaction-Diffusion Computers (Elsevier, New York, 2005)

  24. Encyclopedia of Complexity and Systems Science, edited by R.A. Meyers (Springer, Berlin, 2009)

  25. A. Kolbus, A. Lemarchand, A.L. Kawczynski, B. Nowakowski, Phys. Chem. Chem. Phys. 12, 13224 (2010)

    Article  Google Scholar 

  26. A.L. Kawczynski, J. Gorecki, J. Phys. Chem. 96, 1060 (1992)

    Article  Google Scholar 

  27. A.L. Kawczynski, J. Gorecki, J. Phys. Chem. 97, 10358 (1993)

    Article  Google Scholar 

  28. J. Gorecki, A.L. Kawczynski, J. Phys. Chem. 100, 19371 (1996)

    Article  Google Scholar 

  29. B.V. Vol’ter, I.Ye. Sal’nikov, Modeling and Optimization of Catalytic Processes (Nauka, Moscow, 1965) (in Russian)

  30. B. Nowakowski, A.L. Kawczynski, J. Phys. Chem. A 109, 3134 (2005)

    Article  Google Scholar 

  31. B. Nowakowski, A.L. Kawczynski, Chem. Phys. Chem. 7, 502 (2006)

    Article  Google Scholar 

  32. A.L. Kawczynski, B. Nowakowski, Phys. Chem. Chem. Phys. 10, 289 (2008)

    Article  Google Scholar 

  33. A. Lemarchand, B. Nowakowski, Europhys. Lett. 71, 530 (2005)

    Article  ADS  Google Scholar 

  34. A. Lemarchand, B. Nowakowski, J. Phys.: Condens. Matter 19, 065130 (2007)

    Article  ADS  Google Scholar 

  35. A.L. Kawczynski, B. Nowakowski, Phys. Rev. E 68, 036218 (2003)

    Article  ADS  Google Scholar 

  36. B. Nowakowski, A. Lemarchand, Phys. Rev. E 64, 061108 (2001)

    Article  ADS  Google Scholar 

  37. B. Nowakowski, A. Lemarchand, Physica A 311, 80 (2002)

    Article  ADS  Google Scholar 

  38. D.T. Gillespie, J. Comput. Phys. 22, 403 (1976)

    Article  MathSciNet  ADS  Google Scholar 

  39. T.M. Cover, J.A. Thomas, Elements of Information Theory (John Wiley & Sons Inc., New Jersey, 2006)

  40. I. Goychuk, P. Hänggi, Phys. Rev. E 61, 4272 (2000)

    Article  ADS  Google Scholar 

  41. I. Goychuk, Phys. Rev. E 64, 021909 (2001)

    Article  ADS  Google Scholar 

  42. I. Goychuk, P. Hänggi, Eur. Phys. J. B 69, 29 (2009)

    Article  ADS  Google Scholar 

  43. D.T. Gillespie, J. Phys. Chem. 81, 2340 (1977)

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224, Warsaw, Poland

    Jerzy Gorecki & Bogdan Nowakowski

  2. Faculty of Mathematics and Life Science, UKSW, 01-938, Warsaw, Poland

    Jerzy Gorecki

  3. Physics Laboratory, Warsaw University of Life Sciences, Nowoursynowska 159, 02-776, Warsaw, Poland

    Adam Gorecki & Bogdan Nowakowski

  4. Université Pierre et Marie Curie - Paris 6, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), 4 place Jussieu, case courrier 121, 75252, Paris Cedex 05, France

    Annie Lemarchand

  5. CNRS, LPTMC, UMR, 7600, Paris, France

    Annie Lemarchand

Authors
  1. Jerzy Gorecki
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  2. Adam Gorecki
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  3. Annie Lemarchand
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  4. Bogdan Nowakowski
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Correspondence to Jerzy Gorecki.

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Gorecki, J., Gorecki, A., Lemarchand, A. et al. Information resonance in a model excitable system. Eur. Phys. J. B 86, 264 (2013). https://doi.org/10.1140/epjb/e2013-40054-y

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  • DOI: https://doi.org/10.1140/epjb/e2013-40054-y

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