Skip to main content
SpringerLink
Log in

Escape statistics for systems driven by dichotomous noise. II. The imperfect pitchfork bifurcation as a case study

  • Articles
  • Published:
Journal of Statistical Physics Aims and scope Submit manuscript

Abstract

We use the general results for the escape probabilities and mean exit times obtained in an accompanying paper to analyze in detail a nonlinear system presenting an imperfect (subcritical) pitchfork bifurcation. We redraw the bifurcation diagram to show the effect of the noise. To avoid spurious results we introduce the concept ofextinction level as the minimum possible value for the system, and discuss its effect on the bifurcation diagram.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Ollarea, J. M. R. Parrondo, and F. J. de la Rubia,J. Stat. Phys., this issue, preceding paper.

  2. W. Horsthemke and R. Lefever,Noise-Induced Transitions (Springer-Verlag, Berlin, 1984).

    Google Scholar 

  3. J. Guckenheimer and P. Holmes,Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields (Springer-Verlag, Berlin, 1983).

    Google Scholar 

  4. M. Golubitsky and D. G. Schaeffer,Singularities and Groups in Bifurcation Theory, Vol. 1 (Springer-Verlag, Berlin, 1985).

    Google Scholar 

  5. L. Arnold and W. Kliemann, InProbabilistic Analysis and Rrelated Topics, Vol. 3, A. T. Barucha-Reid, ed. (Academic Press, New York, 1983).

    Google Scholar 

  6. L. Arnold and P Boxler, InDiffusion Processes and Related Problems in Analysis, Vol. II, M. Pinsky and V. Wihstutz, eds. (Birkhauser, Basel, 1991).

    Google Scholar 

  7. L. Arnold, InNonlinear Stochastic Dynamic Engineering Systems, G. I. Schueller and F. Ziegler, eds. (Springer-Verlag, Berlin, 1987).

    Google Scholar 

  8. U. Behn and K. Schiele,Z. Phys. B 77:485 (1989).

    Article  Google Scholar 

  9. A. García-Tejedor, J. C. S. Nuño, J. Olarrea, F. J. de la Rubia, and F. MonteroJ. Theor. Biol. 134:431 (1988).

    Google Scholar 

  10. J. C. Nuño, F. Montero, and F. J. de la Rubia,J. Theor. Biol.,165:553 (1993).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento Matemática Aplicada y Estadística, ETSI Aeronáuticos, Universidad Politécnica de Madrid, 28040, Madrid, Spain

    J. Olarrea

  2. Departamento Física Aplicada I, Facultad de Física, Universidad Complutense, 28040, Madrid, Spain

    J. M. R. Parrondo

  3. Departamento Física Fundamental, Universidad a Distancia, 28080, Madrid, Spain

    F. J. de la Rubia

Authors
  1. J. Olarrea
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. M. R. Parrondo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. F. J. de la Rubia
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to F. J. de la Rubia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Olarrea, J., Parrondo, J.M.R. & de la Rubia, F.J. Escape statistics for systems driven by dichotomous noise. II. The imperfect pitchfork bifurcation as a case study. J Stat Phys 79, 683–699 (1995). https://doi.org/10.1007/BF02184876

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02184876

Key Words

Search

Navigation