Differential delay equations in chemical kinetics: Some simple linear model systems

Abstract

The reasons for and the effects of incorporating time lags into the differential equations of chemical kinetics are investigated for some simple model systems. Complex networks of first-order reactions may, in the limit of long times, be described by relatively simple systems of differential delay (differential difference) equations, in which the effects of intermediates are replaced by time lags. Explicit inclusion of time lags affords a more physically realistic description of nucleation in certain solid state reactions. An electrochemical cell with lagged feedback gives rise to a particularly simple and instructive delay equation. A two-chamber system in which molecules diffuse with a time lag through a membrane shows unexpected oscillatory, and seemingly nonconservative behavior, which is explained in terms of the number of molecules in passage through the membrane.