Number fluctuations and the threshold model of kinetic switches

The dynamics within nanoscale systems, in biological cells, or in macroscopic ecosystems often involves low populations of molecules or members, provoking the need for a discrete description instead of a continuum theory. We consider a classical birth-immigration-death process in such a few number system and show in how far fluctuations become prominent in the system's dynamics. The exact analytical results are investigated and new functions for the characterisation of the population dynamics established. We investigate the corresponding continuum approximation of the process and derive a Fokker-Planck equation for the fluctuations. (C) 2002 Elsevier Science B.V. All rights reserved.