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How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity

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Abstract

A non-linear behavior of dynamic model of the magma-plug system under the action of N-shaped friction force and stochastic disturbances is studied. It is shown that the deterministic dynamics essentially depends on the mutual arrangement of an equilibrium point and the friction force branches. Variations of this arrangement imply bifurcations, birth and disappearance of stable limit cycles, changes of the stability of equilibria, system transformations between mono- and bistable regimes. A slope of the right increasing branch of the friction function is responsible for the formation of such regimes. In a bistable zone, the noise generates transitions between small and large amplitude stochastic oscillations. In a monostable zone with single stable equilibrium, a new dynamic phenomenon of noise-induced generation of large amplitude stochastic oscillations in the plug rate and pressure is revealed. A beat-type dynamics of the plug displacement under the influence of stochastic forcing is studied as well.

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References

  1. R.G. Vaughan, S.J. Hook, M.S. Ramsey, V.J. Realmuto, D.J. Schneider, Geophys. Res. Lett. 32, L19305 (2005)

    Article  ADS  Google Scholar 

  2. H.K.M. Tanaka, T. Kusagaya, H. Shinohara, Nat. Commun. 5, 3381 (2014)

    ADS  Google Scholar 

  3. O.E. Melnik, R.S.J. Sparks, Nature 402, 37 (1999)

    Article  ADS  Google Scholar 

  4. A. Barmin, O. Melnik, R.S.J. Sparks, Earth Planet. Sci. Lett. 199, 173 (2002)

    Article  ADS  Google Scholar 

  5. M. Nakanishi, T. Koyaguchi., J. Volcanol. Geother. Res. 178, 46 (2008)

    Article  ADS  Google Scholar 

  6. A. Costa, G. Wadge, O. Melnik, Earth Planet. Sci. Lett. 337-338, 39 (2012)

    Article  ADS  Google Scholar 

  7. G. Woo, The Mathematics of Natural Catastrophes (Imperial College Press, 2000)

  8. B. Saltzman, Dynamical Paleoclimatology: Generalised Theory of Global Climate Change (Academic Press, San Diego, 2002)

  9. D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko, Tellus A 66, 23454 (2014)

    Article  Google Scholar 

  10. D.V. Alexandrov, I.A. Bashkirtseva, S.P. Fedotov, L.B. Ryashko, Eur. Phys. J. B 87, 227 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  11. R.S.J. Sparks, Earth Planet. Sci. Lett. 210, 1 (2003)

    Article  ADS  Google Scholar 

  12. M.S. Bebbington, W. Marzocchi, J. Geophys. Res. 116, B05204 (2011)

    ADS  Google Scholar 

  13. W. Horstemke, R. Lefever, Noise-Induced Transitions (Springer, Berlin, 1984)

  14. Y.C. Lai, T. Tél, Transient Chaos: Complex Dynamics on Finite Time Scales (Springer, Berlin, 2011)

  15. I. Bashkirtseva, G. Chen, L. Ryashko, Chaos 22, 033104 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  17. M.D. McDonnell, N.G. Stocks, C.E.M. Pearce, D. Abbott, Stochastic Resonance: from Suprathreshold Stochastic Resonance to Stochastic Signal Quantization (Cambridge University Press, Cambridge, 2008)

  18. J.J. Torres, J. Marro, J.F. Mejias, New J. Phys. 13, 053014 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. I. Bashkirtseva, A.B. Neiman, L. Ryashko, Phys. Rev. E 87, 052711 (2013)

    Article  ADS  Google Scholar 

  22. S. Patidar, A. Pototsky, N.B. Janson, New J. Phys. 11, 073001 (2009)

    Article  ADS  Google Scholar 

  23. D.V. Alexandrov, I.A. Bashkirtseva, A.P. Malygin, L.B. Ryashko, Pure Appl. Geophys. 170, 2273 (2013)

    Article  ADS  Google Scholar 

  24. D.A. Kessler, N.M. Shnerb, New J. Phys. 11, 043017 (2009)

    Article  ADS  Google Scholar 

  25. R.P. Denlinger, R.P. Hoblitt, Geology 27, 459 (1999)

    Article  ADS  Google Scholar 

  26. D. Dzurisin, J.W. Vallance, T.M. Gerlach, S.C. Moran, S.D. Malone, Eos Trans. Am. Geophys. Union 86, 25 (2005)

    Article  ADS  Google Scholar 

  27. C. Michaut, Y. Ricard, D. Bercovici, R.S.J. Sparks, Nat. Geosci. 6, 856 (2013)

    Article  ADS  Google Scholar 

  28. J.E. Kendrick, Y. Lavallée, T. Hirose, G. Di Toro, A.J. Hornby, S. De Angelis, D.B. Dingwell, Nat. Geosci. 7, 438 (2014)

    Article  ADS  Google Scholar 

  29. R.M. Iverson, D. Dzurisin, C.A. Gardner, T.M. Gerlach, R.G. LaHusen, M. Lisowski, J.J. Major, S.D. Malone, J.A. Messerich, S.C. Moran, J.S. Pallister, A.I. Qamar, S.P. Schilling, J.W. Vallance, Nature 444, 439 (2006)

    Article  ADS  Google Scholar 

  30. P.L. Moore, N.R. Iverson, R.M. Iverson, U.S. Geological Survey Professional Paper 1750 (2008)

  31. R.S. Matoza, B.A. Chouet, J. Geophys. Res. B 115, 12206 (2010)

    Article  ADS  Google Scholar 

  32. D.V. Alexandrov, I.A. Bashkirtseva, L.B. Ryashko, Nonlin. Processes Geophys. 22, 197 (2015)

    Article  Google Scholar 

  33. P. Hänggi, H. Thomas, Phys. Rep. 88, 207 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  34. P.E. Kloeden, E. Platen, Numerical Solutions of Stochastic Differential Equations (Springer-Verlag, Berlin, 1999)

  35. G.E.P. Box, M.E. Muller, Ann. Math. Stat. 29, 610 (1958)

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematical Physics, Ural Federal University, Lenina ave., 51, 620000, Ekaterinburg, Russia

    Dmitri V. Alexandrov, Irina A. Bashkirtseva & Lev B. Ryashko

Authors
  1. Dmitri V. Alexandrov
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  2. Irina A. Bashkirtseva
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  3. Lev B. Ryashko
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Correspondence to Dmitri V. Alexandrov.

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Alexandrov, D., Bashkirtseva, I. & Ryashko, L. How a small noise generates large-amplitude oscillations of volcanic plug and provides high seismicity. Eur. Phys. J. B 88, 106 (2015). https://doi.org/10.1140/epjb/e2015-60130-6

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  • DOI: https://doi.org/10.1140/epjb/e2015-60130-6

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