Gallinger Cameron, Popovic Lea
Department of Mathematics and Statistics, Concordia University, Montreal, Quebec H3G 1M8, Canada.
R Soc Open Sci. 2024 Oct 23;11(10):231878. doi: 10.1098/rsos.231878. eCollection 2024 Oct.
We consider a general class of autocatalytic reactions, which has been shown to display stochastic switching behaviour (discreteness-induced transitions (DITs)) in some parameter regimes. This behaviour was shown to occur either when the overall species count is low or when the rate of inflow and outflow of species is relatively much smaller than the rate of autocatalytic reactions. The long-term behaviour of this class was analysed in Bibbona (Bibbona 2020 , 20200243 (doi:10.1098/rsif.2020.0243)) with an analytic formula for the stationary distribution in the symmetric case. We focus on the case of asymmetric autocatalytic reactions and provide a formula for an approximate stationary distribution of the model. We show this distribution has different properties corresponding to the distinct behaviour of the process in the three parameter regimes; in the DIT regime, the formula provides the fraction of time spent at each of the stable points.
我们考虑一类一般的自催化反应，这类反应已被证明在某些参数区域会表现出随机切换行为（离散诱导跃迁（DITs））。当总物种数较低或者物种的流入和流出速率相对远小于自催化反应速率时，这种行为就会出现。Bibbona（Bibbona 2020，20200243（doi:10.1098/rsif.2020.0243））分析了这类反应的长期行为，并给出了对称情况下平稳分布的解析公式。我们关注非对称自催化反应的情况，并给出该模型近似平稳分布的公式。我们表明，对应于该过程在三个参数区域的不同行为，这种分布具有不同的性质；在DIT区域，该公式给出了在每个稳定点所花费时间的比例。
