Skip to main content
SpringerLink
Log in

Bistable behaviour in squeezed vacua: II. Stability analysis and chaos

  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Linear stability analysis and (numerical) investigation of the periodic and chaotic self-pulsing behaviour are presented for the Maxwell-Bloch equations of a bistable model in contact with a squeezed vacuum field. Effect of the squeeze phase parameter on the period doubling bifurcation that preceeds chaos is examined for the adiabatic and non-adiabatic regimes.

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. S.S. Hassan, H.A. Batarfi, R. Saunders, R.K. Bullough, Eur. Phys. J. D 8, 403 (2000).

    Article  ADS  Google Scholar 

  2. S.L. McCall, Appl. Phys. Lett. 32, 284 (1978).

    Article  ADS  Google Scholar 

  3. R. Bonifacio, L.A. Lugiato, Lett. Nouvo Cimento 21, 510 (1978).

    Article  Google Scholar 

  4. R. Bonifacio, M. Gronchi, L.A. Lugiato, Opt. Commun. 30, 129 (1979).

    Article  ADS  Google Scholar 

  5. L.A. Lugiato, Opt. Commun. 33, 108 (1980).

    Article  ADS  Google Scholar 

  6. L.A. Lugiato, L.M. Naducci, in Fundamental systems in Quantum Optics, edited by J. Dalibard, J.M. Raimond, J. Zinn-Justin (Elsevier Sci. Publ., Amsterdam, 1992), pp. 942–1047.

    Google Scholar 

  7. L.A. Lugiato, L.M. Narducci, D.K. Brandy, C.A. Pennise, Opt. Commun. 43, 281 (1982).

    Article  ADS  Google Scholar 

  8. H.A. Batarfi, Ph.D. thesis, University of Manchester, 1995.

  9. T.S. Parker, L.O. Chua, Practical Numerical Algorithms For Chaotic Systems (Springer-Verlag, NY, 1989).

    MATH  Google Scholar 

  10. G.D. van Wiggeren, R. Roy, Science 279, 1198 (1998); L. Pecora, Phys. World 11, 25 (April, 1998).

    Article  ADS  Google Scholar 

  11. S.A. Kauffman, Scientifc American 264, 64 (August, 1991).

    Google Scholar 

  12. E. Corcoran, Scientifc American 264, 82 (August, 1991).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Science, Mathematics Department (Women’s Section), King Abdul-Aziz University, P.O. Box 41101, Jeddah, 21521, Saudi Arabia

    H. A. Batarfi

  2. Faculty of Science, Mathematics Department, Ain Shams University, Cairo, Egypt

    S. S. Hassan

  3. Department of Mathematics and Physics, Manchester Metropolitan University, Manchester, M1 5GD, England

    R. Saunders

  4. Mathematics Department, UMIST, P.O. Box 88, Manchester, M60 1QD, England

    R. K. Bullough

Authors
  1. H. A. Batarfi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. S. Hassan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. R. Saunders
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. R. K. Bullough
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Batarfi, H.A., Hassan, S.S., Saunders, R. et al. Bistable behaviour in squeezed vacua: II. Stability analysis and chaos. Eur. Phys. J. D 8, 417–429 (2000). https://doi.org/10.1007/s10053-000-8811-3

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10053-000-8811-3

PACS

Search

Navigation