Analysis of stochastic chemical system close to a SNIPER bifurcation of its mean-field model

0335835 - MÚ 2010 RIV US eng J - Journal Article
Erban, R. - Chapman, S.J. - Kevrekidis, I.G. - Vejchodský, Tomáš
Analysis of stochastic chemical system close to a SNIPER bifurcation of its mean-field model.
Siam Journal on Applied Mathematics. Roč. 70, č. 3 (2009), s. 984-1016. ISSN 0036-1399. E-ISSN 1095-712X
R&D Projects: GA ČR(CZ) GA102/07/0496; GA AV ČR IAA100760702
Institutional research plan: CEZ:AV0Z10190503
Keywords : stochastic bifurcations * chemical Fokker-Planck equation
Subject RIV: BA - General Mathematics
Impact factor: 1.639, year: 2009

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.
Permanent Link: http://hdl.handle.net/11104/0180195