Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks
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Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks. / Anderson, David F. ; Craciun, Gheorghe; Gopalkrishnan , Manoj ; Wiuf, Carsten Henrik.
I: Bulletin of Mathematical Biology, Bind 77, Nr. 9, 2015, s. 1744-1767.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks
AU - Anderson, David F.
AU - Craciun, Gheorghe
AU - Gopalkrishnan , Manoj
AU - Wiuf, Carsten Henrik
PY - 2015
Y1 - 2015
N2 - We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth–death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
AB - We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potential of the stationary distribution of stochastically modeled complex balanced systems. We extend this result to general birth–death models and demonstrate via example that similar scaling limits can yield Lyapunov functions even for models that are not complex or detailed balanced, and may even have multiple equilibria.
U2 - 10.1007/s11538-015-0102-8
DO - 10.1007/s11538-015-0102-8
M3 - Journal article
VL - 77
SP - 1744
EP - 1767
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 9
ER -
ID: 148693029