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Catastrophes

  • Alexander S. Mikhailov
  • Alexander Yu. Loskutov
Part of the Springer Series in Synergetics book series (SSSYN, volume 52)

Abstract

Catastrophes are qualitative changes of established regimes in distributed active systems. Any catastrophe is related to some bifurcation of an attractor which describes the established regime in a given system.

Keywords

Pair Correlation Function Internal Noise Correlation Radius Uniform Steady State Fluctuation Behavior 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 12.1
    R. Thorn: Structural Stability and Morphogenesis (Benjamin, Reading 1975)Google Scholar
  2. 12.2
    T. Poston, I. Stewart: Catastrophe Theory and Its Applications (Pitman, London 1978)zbMATHGoogle Scholar
  3. 12.3
    H. Haken: Synergetics (Springer, Berlin, Heidelberg 1978)zbMATHGoogle Scholar
  4. 12.4
    H. Haken: Advanced Synergetics (Springer, Berlin, Heidelberg 1983)zbMATHGoogle Scholar
  5. 12.5
    A. Nitzan, P. Ortoleva, J. Deutch, J. Ross: J. Chem. Phys. 61, 1056 (1974)ADSCrossRefGoogle Scholar
  6. 12.6
    D. Walgraef, G. Dewel, P. Borckmans: Adv. Chem. Phys. 49, 311 (1982)CrossRefGoogle Scholar
  7. 12.7
    Ya.B. Zeldovich, A.S. Mikhailov: Sov. Phys. Usp. 30, 977–992 (1987)ADSCrossRefGoogle Scholar
  8. 12.8
    L.D. Landau, I.M. Lifshitz: Statistical Physics (Pergamon, Oxford 1980)Google Scholar
  9. 12.9
    S.-K. Ma: Modern Theory of Critical Phenomena (Benjamin, Reading 1976)Google Scholar
  10. 12.10
    S. Grossmann, A.S. Mikhailov: Z. Phys. B 78, 1–10 (1990)ADSCrossRefGoogle Scholar
  11. 12.11
    M.A. Shishkova: Dokl. Akad. Nauk SSSR 209, 576–579 (1973)MathSciNetGoogle Scholar
  12. 12.12
    N.R. Lebovitz, R.J. Schaar: Stud. Appl. Math. 54, 229–260 (1975)MathSciNetzbMATHGoogle Scholar
  13. 12.13
    R. Haberman: SIAM J. Appl. Math. 37, 69–105 (1979)MathSciNetzbMATHCrossRefGoogle Scholar
  14. 12.14
    P. Mandel, H. Zeghlache, T. Emeux: “Time-dependent phase transitions”, in Far from Equilibrium Phase Transitions, ed. by L. Garrido (Springer, Berlin, Heidelberg 1988) pp. 217–235CrossRefGoogle Scholar
  15. 12.15
    G. Nicolis, I. Prigogine: Proc. Natl. Acad. Sci. USA 78, 659 (1981)MathSciNetADSCrossRefGoogle Scholar
  16. 12.16
    D. Kondepudi, I. Prigogine: Physica A 107, 1 (1981)MathSciNetADSCrossRefGoogle Scholar
  17. 12.17
    L.L. Morozov, V.I. Goldanskii: “Violation of symmetry and self-organization in prebiological evolution”, in Self-Organization. Autowaves and Structures Far from Equilibrium, ed. by V.I. Krinsky (Springer, Berlin, Heidelberg 1984) pp. 224–231CrossRefGoogle Scholar
  18. 12.18
    D. Kondepudi, G.W. Nelson: Phys. Rev. Lett. 50, 1013 (1983)ADSCrossRefGoogle Scholar
  19. 12.19
    F. Moss, D. Kondepudi, P.V.F. McClintock: Phys. Lett. A 112, 293 (1985)ADSCrossRefGoogle Scholar
  20. 12.20
    G. Broggi, A. Colombo, L.A. Lugiato, P. Mandel: Phys. Rev. A 33, 3635–3637 (1986)ADSCrossRefGoogle Scholar
  21. 12.21
    H. Zeghlache, P. Mandel, C. van den Broeck: Phys. Rev. A 40, 286–294 (1989)ADSCrossRefGoogle Scholar
  22. 12.22
    W. Horsthemke, M. Malek-Mansour: Z. Phys. B 24, 307 (1976)ADSCrossRefGoogle Scholar
  23. 12.23
    W. Horsthemke, R. Lefever: Noise-Induced Transitions (Springer, Berlin, Heidelberg 1984)zbMATHGoogle Scholar
  24. 12.24
    Ya.B. Zeldovich, S.A. Molchanov, A.A. Ruzmaikin, D.D. Sokoloff: Proc. Natl. Acad. Sci. USA 84, 6323 (1987)MathSciNetADSCrossRefGoogle Scholar
  25. 12.25
    A.S. Mikhailov: Phys. Rep. 184, 307–374 (1989)ADSCrossRefGoogle Scholar
  26. 12.26
    A.S. Mikhailov: “Fluctuations and critical phenomena in reaction-diffusion systems”, in Far from Equilibrium Phase Transitions, ed. by L. Garrido (Springer, Berlin, Heidelberg 1988) pp. 139–156CrossRefGoogle Scholar
  27. 12.27
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. JETP 52, 989 (1980)ADSGoogle Scholar
  28. 12.28
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. JETP 57, 863 (1983)Google Scholar
  29. 12.29
    A.S. Mikhailov, I.V. Uporov: Sov. Phys. Usp. 27, 695 (1984)ADSCrossRefGoogle Scholar
  30. 12.30
    V.R. Chechetkin, V.S. Lutovinov: Nuovo Cimento B 99, 103–116 (1987)ADSCrossRefGoogle Scholar
  31. 12.31
    V.R. Chechetkin, V.S. Lutovinov: Z. Phys. B 69, 129–135 (1987)MathSciNetADSCrossRefGoogle Scholar
  32. 12.32
    H.K. Janssen: Z. Phys. B 42, 151 (1981)ADSCrossRefGoogle Scholar
  33. 12.33
    H.K. Janssen: Z. Phys. B 58, 311 (1985)MathSciNetADSCrossRefGoogle Scholar
  34. 12.34
    A.S. Mikhailov: Dokl. Akad. Nauk SSSR 243, 786 (1978)Google Scholar
  35. 12.35
    A.S. Mikhailov: Phys. Lett. A 73, 143 (1979)MathSciNetADSCrossRefGoogle Scholar
  36. 12.36
    A.S. Mikhailov: Z. Phys. B 41, 277 (1981)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Alexander S. Mikhailov
    • 1
    • 2
  • Alexander Yu. Loskutov
    • 1
  1. 1.Department of PhysicsMoscow State UniversityMoscowUSSR
  2. 2.Institut für Theoretische Physik und SynergetikUniversität StuttgartStuttgart 80Fed. Rep. of Germany

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