• Login
    View Item 
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • View Item
    •   Home
    • Office of Sponsored Research (OSR)
    • KAUST Funded Research
    • Publications Acknowledging KAUST Support
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Browse

    All of KAUSTCommunitiesIssue DateSubmit DateThis CollectionIssue DateSubmit Date

    My Account

    Login

    Quick Links

    Open Access PolicyORCID LibguidePlumX LibguideSubmit an Item

    Statistics

    Display statistics

    Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model

    • CSV
    • RefMan
    • EndNote
    • BibTex
    • RefWorks
    Type
    Article
    Authors
    Erban, Radek
    Chapman, S. Jonathan
    Kevrekidis, Ioannis G.
    Vejchodský, Tomáš
    KAUST Grant Number
    KUK-C1-013-04
    Date
    2009-01
    Permanent link to this record
    http://hdl.handle.net/10754/597550
    
    Metadata
    Show full item record
    Abstract
    A framework for the analysis of stochastic models of chemical systems for which the deterministic mean-field description is undergoing a saddle-node infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs, for example, in the modeling of cell-cycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the mean-field model does not oscillate. The dependence of the mean period of these oscillations on the parameters of the model (kinetic rate constants) and the size of the system (number of molecules present) are studied. Our approach is based on the chemical Fokker-Planck equation. To gain some insight into the advantages and disadvantages of the method, a simple one-dimensional chemical switch is first analyzed, and then the chemical SNIPER problem is studied in detail. First, results obtained by solving the Fokker-Planck equation numerically are presented. Then an asymptotic analysis of the Fokker-Planck equation is used to derive explicit formulae for the period of oscillation as a function of the rate constants and as a function of the system size. © 2009 Society for Industrial and Applied Mathematics.
    Citation
    Erban R, Chapman SJ, Kevrekidis IG, Vejchodský T (2009) Analysis of a Stochastic Chemical System Close to a SNIPER Bifurcation of Its Mean-Field Model. SIAM Journal on Applied Mathematics 70: 984–1016. Available: http://dx.doi.org/10.1137/080731360.
    Sponsors
    Received by the editors July 28, 2008; accepted for publication ( in revised form) June 9, 2009; published electronically August 21, 2009. This work is based on work supported by St. John's College, Oxford; Linacre College, Oxford; Somerville College, Oxford; and by award KUK-C1-013-04, given by King Abdullah University of Science and Technology (KAUST) (RE).
    Publisher
    Society for Industrial & Applied Mathematics (SIAM)
    Journal
    SIAM Journal on Applied Mathematics
    DOI
    10.1137/080731360
    ae974a485f413a2113503eed53cd6c53
    10.1137/080731360
    Scopus Count
    Collections
    Publications Acknowledging KAUST Support

    entitlement

     
    DSpace software copyright © 2002-2021  DuraSpace
    Quick Guide | Contact Us | Send Feedback
    Open Repository is a service hosted by 
    Atmire NV
     

    Export search results

    The export option will allow you to export the current search results of the entered query to a file. Different formats are available for download. To export the items, click on the button corresponding with the preferred download format.

    By default, clicking on the export buttons will result in a download of the allowed maximum amount of items. For anonymous users the allowed maximum amount is 50 search results.

    To select a subset of the search results, click "Selective Export" button and make a selection of the items you want to export. The amount of items that can be exported at once is similarly restricted as the full export.

    After making a selection, click one of the export format buttons. The amount of items that will be exported is indicated in the bubble next to export format.