BISTABILITY WITHOUT HYSTERESIS IN CHEMICAL-REACTION SYSTEMS - A THEORETICAL-ANALYSIS OF IRREVERSIBLE TRANSITIONS BETWEEN MULTIPLE STEADY-STATES

The coexistence between two stable steady states, referred to as bista bility, is generally associated with a phenomenon of hysteresis in whi ch a system jumps back and forth between the two branches of stable st ates for different, critical values of some control parameter, corresp onding to two limit points. We focus here on the cases where the trans itions between the two branches of stable steady states become irrever sible when one of the limit points becomes inaccessible or goes to inf inity; we refer to these two cases as irreversible transitions of type 1 or 2, respectively. In order to study in detail the conditions in w hich such irreversible transitions between multiple steady states occu r in chemical systems, we analyze two models based on reversible chemi cal steps. The first model, due to Schlogl, has long been studied as a simple prototype for bistability. This model is shown to admit irreve rsible transitions of type 1 as one of the limit points associated wit h bistability moves into a physically inaccessible region of negative values of a control parameter. A second, original model is proposed, t o illustrate the case of irreversible transitions of type 2 in which a limit point goes to infinity. Irreversible transitions of type 1 can also occur in this model, as a function of other control parameters. I n both models irreversible transitions take place under nonequilibrium conditions. The analysis indicates what reaction steps need to remain reversible in the models in order to preserve the irreversible transi tions.