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

0335835 - MÚ 2010 RIV US eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA102/07/0496; GA AV ČR IAA100760702
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: stochastic bifurcations * chemical Fokker-Planck equation
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 1.639, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0180195