Stationary distributions of systems with discreteness-induced transitions
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Stationary distributions of systems with discreteness-induced transitions. / Bibbona, Enrico; Kim, Jinsu; Wiuf, Carsten.
In: Journal of the Royal Society Interface, Vol. 17, No. 168, 20200243, 2020.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - Stationary distributions of systems with discreteness-induced transitions
AU - Bibbona, Enrico
AU - Kim, Jinsu
AU - Wiuf, Carsten
PY - 2020
Y1 - 2020
N2 - We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.
AB - We provide a theoretical analysis of some autocatalytic reaction networks exhibiting the phenomenon of discreteness-induced transitions. The family of networks that we address includes the celebrated Togashi and Kaneko model. We prove positive recurrence, finiteness of all moments and geometric ergodicity of the models in the family. For some parameter values, we find the analytic expression for the stationary distribution and discuss the effect of volume scaling on the stationary behaviour of the chain. We find the exact critical value of the volume for which discreteness-induced transitions disappear.
KW - discreteness-induced transitions
KW - reaction networks
KW - stationary distributions
UR - http://www.scopus.com/inward/record.url?scp=85090117488&partnerID=8YFLogxK
U2 - 10.1098/rsif.2020.0243rsif20200243
DO - 10.1098/rsif.2020.0243rsif20200243
M3 - Journal article
AN - SCOPUS:85090117488
VL - 17
JO - Journal of the Royal Society. Interface
JF - Journal of the Royal Society. Interface
SN - 1742-5689
IS - 168
M1 - 20200243
ER -
ID: 248329340