Journal of the Physical Society of Japan
Online ISSN : 1347-4073
Print ISSN : 0031-9015
ISSN-L : 0031-9015
Stochastic Approach to Nonlinear Chemical Reactions Having Multiple Steady States
Ken’ichi Nishiyama
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ジャーナル 認証あり

1974 年 37 巻 1 号 p. 44-49

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抄録
A stochastic approach is carried out to nonlinear chemical reactions having multiple steady states. The reaction processes are assumed to be Markovian and normal approximation is adopted. It is shown that the steady states and their stability conditions are the same as those obtained from the deterministic approach when the volume of the system is large compared with order 1. Furthermore it is obtained from the machine calculation that even if the volume is large the transition from an initial state near the unstable steady state to the stable one is not always possible. And there seems to be a sort of threshold. If the state is too close to the unstable steady state, then the fluctuations of the chemical substances become divergent and the transition can not be seen. When the the transition is possible, the fluctuations will pass through a maximum on the way.
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