Phase Transition, Stability, and Oscillations for an Autocatalytic, Single, First-Order Reaction in a Membrane

Abstract

Oscillations of $p\mathrm{H}$ in an enzyme-catalyzed unbuffered hydrolysis reaction in a one-dimensional membrane are characterized by two parameters: the boundary substrate concentration, ${S_0}^{*}$, and a new phase transition parameter, $\zeta$ [Eq. (9)]. We present nonlinear computer simulations with and without a boundary layer, a linear theory for small amplitude oscillations without a boundary layer, and comments on recent experiments.