Skip to main content

Noise-Induced Nonequilibrium Phase Transitions

  • Chapter
  • 698 Accesses

Part of the book series: Springer Series in Synergetics ((SSSYN,volume 15))

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Chapter 6

  1. M. Lavrentiev, B. Chabat: Méthodes de la théorie des fonctions d’une variable complexe (Mir, Moscow 1972)

    Google Scholar 

  2. G. Nicolis, R. Lefever: Comment on the kinetic potential and the Maxwell construction in nonequilibrium chemical phase transitions. Phys. Lett. A62, 469 (1977)

    ADS  Google Scholar 

  3. R. Landauer: Fluctuations in bistable tunnel diode circuits. J. Appl. Phys. 33, 2209 (1962)

    Article  ADS  Google Scholar 

  4. R. Thorn: Stabilité structurelle et morphogénèse (Ediscience, Paris 1973); Structural Stability and Morphogenesis (Benjamin, Reading, MA 1975)

    Google Scholar 

  5. T. Poston, I. Stewart: Catastrophe Theory and Its Applications (Pitman, London 1978)

    MATH  Google Scholar 

  6. S.K. Ma: Modern Theory of Critical Phenomena (Benjamin, Reading, MA 1976)

    Book  Google Scholar 

  7. W. Horsthemke, M. Malek Mansour: The influence of external noise on nonequilibrium phase transitions. Z. Phys. B24, 307 (1976)

    ADS  Google Scholar 

  8. L. Arnold, W. Horsthemke, R. Lefever: White and coloured external noise and transition phenomena in nonlinear systems. Z. Phys. B29, 867 (1978)

    Google Scholar 

  9. W. Ebeling: Nonequilibrium transitions and stationary probability distributions of stochastic processes. Phys. Lett. A68, 430 (1978)

    MathSciNet  ADS  Google Scholar 

  10. N.S. Goel, N. Richter-Dyn: Stochastic Models in Biology (Academic, New York 1974)

    Google Scholar 

  11. S. Karlin, U. Lieberman: Random temporal variation in selection intensities: case of large population size. Theor. Popul. Biol. 6, 355 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  12. B. Levikson, S. Karlin: Random temporal variation in selection intensities acting on infinite diploid population: diffusion method analysis. Theor. Popul. Biol. 8, 292 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  13. J.H. Gillepsie: Polymorphism in patchy environments. Am. Nat. 108, 145 (1974)

    Article  Google Scholar 

  14. J.H. Gillepsie: The role of the environmental grain in the maintainance of genetic variation. Am. Nat. 108, 831 (1974)

    Article  Google Scholar 

  15. J.H. Gillepsie: The role of migration in the genetic structure of populations in temporally and spatially varying environments II. Island models. Theor. Popul. Biol. 10, 227 (1976)

    Article  Google Scholar 

  16. J.H. Gillepsie, C. Langley: Multi-locus behavior in random environments I. Random Levene models. Genetics 82, 123 (1976)

    MathSciNet  Google Scholar 

  17. W.J. Ewens: Mathematical Population Genetics. Biomathematics, Vol.9 (Springer, Berlin, Heidelberg, New York 1979)

    MATH  Google Scholar 

  18. M. Kimura, T. Ohta: Theoretical Aspects of Population Genetics (University Press, Princeton, NJ 1971)

    MATH  Google Scholar 

  19. M.O. Hongler: Exact time dependent probability density for a nonlinear non-Markovian stochastic process. Helv. Phys. Acta 52, 280 (1979)

    MathSciNet  Google Scholar 

  20. J. Elliott: Eigenfunction expansions associated with singular differential operators. Trans. Am. Math. Soc. 78, 406 (1955)

    Article  MATH  Google Scholar 

  21. R. Courant, D. Hilbert: Methoden der mathematischen Physik I (Springer, Berlin, Heidelberg, New York 1968)

    MATH  Google Scholar 

  22. K. Yosida: Lectures on Differential and Integral Equations (Interscience, New York 1960)

    MATH  Google Scholar 

  23. E.A. Coddington, N. Levinson: Theory of Ordinary Differential Equations (McGraw-Hill, New York 1955)

    MATH  Google Scholar 

  24. E. Hille: Lectures on Ordinary Differential Equations (Addison-Wesley, Reading, MA 1969)

    MATH  Google Scholar 

  25. E. Wong: The construction of a class of stationary Markoff processes. Proc. Symp. Appl. Math. 16, 264 (1964)

    MATH  Google Scholar 

  26. A. Erdelyi: Higher Transcendental Functions, Vols. 1 and 2 (McGraw-Hill, New York 1953)

    Google Scholar 

  27. Prajneshu: Time-dependent solution of the logistic model for population growth in random environment. J. Appl. Probab. 17, 1083 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  28. A. Schenzle, H. Brand: Multiplicative stochastic processes in statistical physics. Phys. Lett. A69, 313 (1979); Phys. Rev. A20, 1628 (1979)

    MathSciNet  ADS  Google Scholar 

  29. M. Suzuki, K. Kaneko, F. Sasagawa: Phase transition and slowing down in non-equilibrium stochastic processes. Prog. Theor. Phys. 65, 828 (1981)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. W. Horsthemke: “Noise Induced Transitions,” in Stochastic Nonlinear Systems in Physics, Chemistry, and Biology, Springer Ser. Synergetics, Vol.8, ed. by L. Arnold, R. Lefever (Springer, Berlin, Heidelberg, New York 1981) p.116

    Google Scholar 

  31. H. Fujisaka, S. Grossmann: External noise effects on the fluctuation line width. Z. Phys. B43, 69 (1981)

    Article  ADS  Google Scholar 

  32. L. Brenig, V. Fairen: Analytical approach to initial-value problems in non linear systems. J. Math. Phys. 22, 649 (1981)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. L. Brenig, N. Banai: Nonlinear dynamics of systems coupled with external noise: some exact results. Physica D5, 208 (1982)

    MathSciNet  ADS  Google Scholar 

  34. R. Graham, A. Schenzle: Carleman imbedding of multiplicative stochastic processes. Phys. Rev. A25, 1731 (1982)

    MathSciNet  ADS  Google Scholar 

  35. M.O. Hongler: Diffusion in a class of double-well potentials-Exact Results. Phys. Lett. 91A, 396 (1982)

    ADS  Google Scholar 

  36. M.O. Hongler, W.M. Zheng: Exact solution for the diffusion in bistable potentials. J. Stat. Phys. 29, 317 (1982)

    Article  MATH  MathSciNet  ADS  Google Scholar 

Download references

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

(2006). Noise-Induced Nonequilibrium Phase Transitions. In: Noise-Induced Transitions. Springer Series in Synergetics, vol 15. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-36852-3_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-36852-3_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11359-1

  • Online ISBN: 978-3-540-36852-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics