Skip to main content
SpringerLink
Log in

Noise induced bifurcations in simple nonlinear models

  • Part V: Theoretical Physics
  • Conference paper
  • First Online:
Book cover Nonlinear Coherent Structures in Physics and Biology

Part of the book series: Lecture Notes in Physics ((LNP,volume 393))

  • 176 Accesses

Abstract

For two generalizations of the Stratonovich model with Gaussian white noise (GWN) and dichotomous Markovian process (DMP) the stationary probability density and moments are calculated. The bifurcation pattern of the stationary solution can be changed qualitativly by varying the deterministic or the noise parameters. We show cases where noise induced states and a subcritical bifurcation can be detected only from the knowledge of the variance.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Kitahara, K.; Horsthemke,W.; Lefever,R.: Phys.Lett. 70A (1979) 377

    Google Scholar 

  2. Kitahara,K.; Horsthemke,W.; Lefever,R.; Inaba,Y.: Prog.Theor.Phys. 64 (1980) 1233

    Google Scholar 

  3. Klyatskin,V.I.: Izv.VUZ Radiofiz. (UdSSR) 20 (1977) 562

    Google Scholar 

  4. Pawula,R.F.: IEEE Trans. Inf.Theory 13 (1967) 33

    Google Scholar 

  5. Pawula,R.F.: Internat.J.Control 25 (1977) 238

    Google Scholar 

  6. Pomeau,Y.: J.Stat.Phys. 24 (1981) 189

    Google Scholar 

  7. Sancho,J.M.; San Miguel,M.: Prog.Theor.Phys. 69 (1983) 1085

    Google Scholar 

  8. Behn,U.;Schiele,K.;Teubel,A.:Wiss.Z.KMU Math.-Naturwiss.R. 34 (1985) 6

    Google Scholar 

  9. Teubel,A.; Behn,U.; Kühnel,A.: Z.Phys.B Condensed Matter 71 (1988) 393

    Article  Google Scholar 

  10. Behn,U.; Schiele,K.: Dubna-Preprint EE 17-84-300 (1984)

    Google Scholar 

  11. Stratonovich,R.L.: Topics in the theory of random noise. Gordon and Breach New York 1967 Vol.2

    Google Scholar 

  12. Abramowitz,M.;Stegun,I.A. (eds):Pocketbook of mathematical functions. Thun, Frankfurt/Main Deutsch 1984

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sektion Physik der Universität Leipzig, Augustusplatz 10, 0-7010, Leipzig, Germany

    Karen Lippert, Konrad Schiele, Ulrich Behn & Adolf Kühnel

Authors
  1. Karen Lippert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Konrad Schiele
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ulrich Behn
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Adolf Kühnel
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

M. Remoissenet M. Peyrand

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag

About this paper

Cite this paper

Lippert, K., Schiele, K., Behn, U., Kühnel, A. (1991). Noise induced bifurcations in simple nonlinear models. In: Remoissenet, M., Peyrand, M. (eds) Nonlinear Coherent Structures in Physics and Biology. Lecture Notes in Physics, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54890-4_184

Download citation

  • DOI: https://doi.org/10.1007/3-540-54890-4_184

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54890-4

  • Online ISBN: 978-3-540-46458-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation