BISTABILITY WITHOUT HYSTERESIS IN CHEMICAL-REACTION SYSTEMS - THE CASE OF NONCONNECTED BRANCHES OF COEXISTING 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, correspo nding to two limit points. In a previous publication (Guidi, G.; Goldb eter, A. J. Phys. Chem. A 1997, 101, 9367) we focused on the cases whe re one of the limit points becomes inaccessible or goes to infinity. U nder such conditions it becomes impossible to achieve the transitions between the two branches of stable steady states as a result of variat ion of a single parameter: bistability ceases to be associated with hy steresis. We referred to these two cases as irreversible transitions o f type 1 or type 2, respectively. To study in detail the conditions un der which such irreversible transitions between multiple steady states occur in chemical systems, two models based on fully reversible chemi cal steps were considered. The first model, due to Schlogl, was shown to admit irreversible transitions of type 1 as one of the limit points associated with bistability moves into a physically inaccessible regi on of negative values of a control parameter. A second, original model was proposed to illustrate the case of irreversible transitions of ty pe 2 in which a limit point goes to infinity. Here, by fusing these tw o models, we construct a hybrid model to analyze the conditions in whi ch irreversible transitions of types 1 and 2 both occur as a function of a given control parameter. Then bistability still exists, but the b ranches of coexisting steady states cease to be connected so that the transitions between the two stable steady states can no longer be achi eved, regardless of the direction of variation in the control paramete r. Such transitions might only result from a change in some other cont rol parameter or from chemical perturbation.