Diffusion-induced instability in chemically reacting systems: Steady-state multiplicity, oscillation, and chaos

The dynamical behavior of two coupled cells or reactors is described. The cells are coupled by diffusion, e.g., through a semipermeable membrane, and the chemical reactions and initial or feed concentrations of all species are the same in the two cells. Each cell has only a single stable steady state in the absence of coupling, and the coupled system may exhibit multiple steady states, periodic oscillation, or chaos. The attractors of the coupled system may be either homogeneous (the two cells have equal concentrations) or inhomogeneous. Three two-variable kinetic models are examined: the Brusselator, a model of the chlorine dioxide-iodine-malonic acid reaction, and the Degn-Harrison model. The dynamical behavior of the coupled system is determined by the nonlinearities in the uncoupled subsystems and by two ratios, that of the diffusion constants of the two species and that of the area of the membrane to the product of the membrane thickness and the volume of a cell.