Stochastic Brusselator model

The Brusselator model (Prigogine Lefever, 1968) is a formal reaction scheme  

The necessary and suflScient condition of the stability of the stationary point is 5 1 + It can be shown for this system that an unstable stationary point implies a limit cycle. 

Stationary and time-dependent solutions of the master equation of the Brusselator have been approximately established by Turner (1979). The main point of his procedure is that the stationary solution of the master equation can be seen as a time average over a period of the limit cycle of P y(t), the time-dependent solution. Some illustrative results of the symmetry-breaking bifurcations in the stochastic Brusselator model are shown in Fig. 5.6 (after Nicolis, 1984). 

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