Complex kinetics of systems with multiple stationary states at equilibrium

Abstract

We consider chemical reactions which at equilibrium have multiple stationary states due to nonidealities of chemical species. When such reactions are included in a simple reaction mechanism open to mass flow, without autocatalysis or feedback steps, there may occur complex dynamics such as relaxation oscillations, as reported earlier for regular solutions. Here we consider both regular solution and ionic species (Debye–Hückel nonideality), show that chemical oscillations may occur arbitrarily close to chemical equilibrium, and trace the topological structure of the complex dynamics of relaxation oscillations, sustained oscillations, stable focus, and stable nodes to the multiplicity of equilibrium states, for stated constraints. Relaxation oscillations occur around an unstable stationary state which, on approach to equilibrium, connects to an unstable equilibrium state. Thus, there is no bifurcation to oscillations on removing the systems from equilibrium. Neither is there a region where linear irreversible thermodynamics is valid close to equilibrium. Earlier work on ionic systems is found to be in error.