Bistable stochastic biochemical networks: large chemical networks and systems with many molecules

Abstract

In this paper we continue the program started in Hwang and Velazquez (J Math Chem, to appear). We describe some chemical systems exhibiting bistable behavior with reaction constants of order one, but where bistability is due to the presence of a large number of chemical species or a large number of molecules of some of the species. We derive generalizations of the classical Kramers' formula that gives the switching times for some particular systems exhibiting a large number of species.