No abstract

The effect of fluctuations on the dynamics of a model of a bistable thermochemical system is studied by means of the master equation. The system has three stationary states and exhibits two types of bistability: the coexistence of two stable focuses and the coexistence of a stable focus with a stable limit cycle separated by a saddle point. Stochastic effects are important when the system is close to the bifurcation, in which the stable limit cycle disappears through a homoclinic orbit. In this case the distribution of the first passage time from the stable limit cycle to the stable focus has a multipeak form. The dependence of this distribution on the number of particles is presented. Near the homoclinic orbit bifurcation, the system also exhibits excitability due to a particular shape of the basin of attraction of the stable focus.

The Belousov−Zhabotinsky reaction (bromate−malonic acid−ferroin) exhibits regular sequences of complex (large and small amplitude) transient oscillations in a CSTR as well as in a batch reactor. General features of the dynamics in both type experiments are explained in a qualitative way using a simple model proposed recently for batch conditions.