Abstract
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.
| Original language | English |
|---|---|
| Journal | Bulletin of Mathematical Biology |
| Volume | 77 |
| Issue number | 9 |
| Pages (from-to) | 1744-1767 |
| Number of pages | 24 |
| ISSN | 0092-8240 |
| DOIs | |
| Publication status | Published - 1 Sept 2015 |
Keywords
- Kinetics
- Markov Chains
- Mathematical Concepts
- Metabolic Networks and Pathways
- Models, Biological
- Population Dynamics
- Stochastic Processes
- Journal Article
- Research Support, N.I.H., Extramural
- Research Support, Non-U.S. Gov't
- Research Support, U.S. Gov't, Non-P.H.S.