Detection of forecoming bifurcations in plasma on the basis of prebifurcation noise enhancement phenomenon (project 2.1)

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• Detection of forecoming bifurcations in plasma
  on the basis of prebifurcation noise enhancement
  phenomenon (project 2.1)
• Research group
• Prof. S. Berczynski, Szczecin University of
  Technology
• Prof.. Yu.A.Kravtsov, Maritime University of
  Szczecin
• Dr. habil. Elena Surovyatkina, Space Research
  Institute, Russ. Acad.Sci., Moscow
• Potential partners
• Ph. Ghendrih and X. Garbet,, France, CEA and
• L. Villard, Switzerland.

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• The concept of the NOISE PRECURSOR for forecomig
  bifurcations was introduced first by Wiesenfeld
  (1996). The linear theory of Wiesenfeld predicts
  the infinite growth of fluctuations near
  bifurcation threshold.
• Nonlinear theory was developed by the joint
  efforts of MUS, SUT and Space Research Institute
  (Moscow). Nonlinear theory implies SATURATION
  FOR FLUCTUATIONS GROWTH near the bifurcation
  threshold and thereby makes the problem of
  bifurcation prediction more realistic.

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Example bifurcation of period doubling in the
nonlinear map
Map
T1
T2

• Bifurcation Diagram

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Rysunek
Bifurcation diagram
x
?
Control parameter
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Bifurcation of the symmetry breaking in the
nonlinear oscillator

• Equation for nonlinear oscillator

Blt0
Bgt0
albo
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• Bifurcations, which take place in a hot plasma
  (information from Dr. L. Villard, Switzerland.)
  
• ELM sequences,
• L-H transitions,
• NTM hysteresis,
• Equilibrium bifurcations.
• Practical problem lack of funds for trips to the
  Euratom Research Centers to initiate the joint
  studies of the experimental materials on
  bifurcations.
• (Fresh example Invitation from Dr.Ph. Ghendrih,
  Cardache, to participate in Pedestal conference
  in France, 4-6 April 2006)

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• Publications
• 1. Kravtsov Yu.A., Belchinskaia S.G., Butkovskii
  O.Ya., Rychka I.A., Surovyatkina E.D.
  Prebifurcational noise rise in nonlinear systems.
  JETP, 2001, 93(6), 1323-1329.
• 2. Yu.A. Kravtsov, E.D.Surovyatkina. Nonlinear
  saturation of prebifurcation noise amplification.
  Phys. Lett. A, 2003, 319(3-4), 348-351.
• 3. E.D.Surovyatkina. Rise and saturation of the
  correlation time near bifurcation threshold.
  Phys. Lett. A, 2004, 323(2), 128-134.
• 4. Yu.A.Kravtsov, S.G.Bilchinskaia, I.A.Rychka,
  E.D.Surovyatkina. Phenomenon of prebifurcation
  noise enhancement as diagnostic instrument for
  plasma systems, influenced by external noise.
  Plasma-2003, CBK PAN, Warszawa, 8-12 Sept. 2003
• 5. S.Berczynski, Yu.A.Kravtsov, E.D.Surovyatkina.
  Fluctuations enhancement ar a precursor of
  bifurcations in nonlinear systems. VIII School of
  Modal Analysis, AGH, Kraków, 1-2 Dec. 2003, pp.
  7-12.
• 6.Surovyatkina E.D., Kravtsov Yu.A., Kurths J.
  Fluctuation growth and saturation in nonlinear
  oscillator on the threshold of bifurcation. Phys.
  Rev. E, 2005, 72(4), 046125, pp.1-7.