IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v88y1977i2p191-214.html
   My bibliography  Save this article

Stochastic theory of nonlinear rate processes with multiple stationary states

Author

Listed:
  • Oppenheim, Irwin
  • Shuler, Kurt E.
  • Weiss, George H.

Abstract

A comparison has been made between the deterministic and stochastic (master equation) formulation of nonlinear chemical rate processes with multiple stationary states. We have shown, via two specific examples of chemical reaction schemes, that the master equations have quasi-stationary state solutions which agree with the various initial condition dependent equilibrium solutions of the deterministic equations. The presence of fluctuations in the stochastic formulation leads to true equilibrium solutions, i.e. solutions which are independent of initial conditions as t → ∞. We show that the stochastic formulation leads to two distinct time scales for relaxation. The mean time for the reaction system to reach the quasi-stationary states from any initial state is of O(N0) where N is a measure of the size of the reaction system. The mean time for relaxation from a quasi-stationary state to the true equilibrium state is O(eN). The results obtained from the stochastic formulation as regards the number and location of the quasi-stationary states are in complete agreement with the deterministic results.

Suggested Citation

  • Oppenheim, Irwin & Shuler, Kurt E. & Weiss, George H., 1977. "Stochastic theory of nonlinear rate processes with multiple stationary states," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 88(2), pages 191-214.
    • Handle: RePEc:eee:phsmap:v:88:y:1977:i:2:p:191-214
    DOI: 10.1016/0378-4371(77)90001-2
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0378437177900012
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/0378-4371(77)90001-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Edmond Langer, 1966. "The ECONOMIC IMPORTANCE OF PUBLIC ENTERPRISE IN BELGIUM," Annals of Public and Cooperative Economics, Wiley Blackwell, vol. 37(1), pages 65-76, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. van Doorn, Erik A. & Pollett, Philip K., 2013. "Quasi-stationary distributions for discrete-state models," European Journal of Operational Research, Elsevier, vol. 230(1), pages 1-14.
    2. Wierman, John C. & Marchette, David J., 2004. "Modeling computer virus prevalence with a susceptible-infected-susceptible model with reintroduction," Computational Statistics & Data Analysis, Elsevier, vol. 45(1), pages 3-23, February.
    3. Ross, J.V. & Pollett, P.K., 2010. "Simple rules for ranking and optimally managing metapopulations," Ecological Modelling, Elsevier, vol. 221(21), pages 2515-2520.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Wonneberger, W., 1980. "On the rate theory for thermal soliton generation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 103(3), pages 543-557.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:88:y:1977:i:2:p:191-214. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.