Spatial structures in dissipative systems

Abstract

A one‐dimensional system which exhibits a chemical instability with respect to free diffusion is analyzed numerically. Below a critical size the homogeneous state is stable. Above this size a succession of inhomogeneous states appear, each one stable over a range of values for the dimension of the system. A plot of the rate of entropy production for the system versus the dimension of the system is monotone increasing but with a change in slope at the appearance of the first inhomogeneous steady state. Transitions between inhomogeneous steady states result in a step increase in the rate of entropy production. At least one additional series of steady states is stable for the system. The results are used to present a model for a chemical signal to initiate cell division.