Erban, R. and Chapman, S. J. and Kevrekidis, I. G. and Vejchodsky, T. (2009) Analysis of a stochastic chemical system close to a sniper bifurcation of its mean field model. Not specified . (Submitted)

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Abstract
A framework for the analysis of stochastic models of chemical systems for which the deterministic meanfield description is undergoing a saddlenode infinite period (SNIPER) bifurcation is presented. Such a bifurcation occurs for example in the modelling of cellcycle regulation. It is shown that the stochastic system possesses oscillatory solutions even for parameter values for which the meanfield 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) is studied. Our approach is based on the chemical Fokker Planck equation. To get some insights into advantages and disadvantages of the method, a simple onedimensional chemical switch is first analyzed, before the chemical SNIPER problem is studied in detail. First, results obtained by solving the FokkerPlanck equation numerically are presented. Then an asymptotic analysis of the FokkerPlanck 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.
Item Type:  Article 

Subjects:  D  G > General 
Research Groups:  Oxford Centre for Collaborative Applied Mathematics 
ID Code:  837 
Deposited By:  Dr M. Stoll 
Deposited On:  08 Oct 2009 16:20 
Last Modified:  29 May 2015 18:31 
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