Exponential equilibration of genetic circuits using entropy methods
Analysis of PDEs
2019-04-12 v1
Abstract
We analyse a continuum model for genetic circuits based on a partial integro-differential equation initially proposed in Friedman, Cai \& Xie (2006) as an approximation of a chemical master equation. We use entropy methods to show exponentially fast convergence to equilibrium for this model with explicit bounds. The asymptotic equilibration for the multidimensional case of more than one gene is also obtained under suitable assumptions on the equilibrium stationary states. The asymptotic equilibration property for networks involving one and more than one gene is investigated via numerical simulations.
Cite
@article{arxiv.1802.02403,
title = {Exponential equilibration of genetic circuits using entropy methods},
author = {José A. Cañizo and José A. Carrillo and Manuel Pájaro},
journal= {arXiv preprint arXiv:1802.02403},
year = {2019}
}
Comments
28 pages, 11 figures