Brusselator simplified

In this simplified version of the Brusselator model, the trimolecular autocatalytic step, which is a necessary condition for the existence of instabilities, is, of course, retained. However, the linear source-sink reaction steps A—>X—>E are suppressed. A continuous flow of X inside the system may still be ensured through the values maintained at the boundaries. The price of this simplification is that (36) can never lead to a homogeneous time-periodic solution. The homogeneous steady states are... 

Much use has been, and continues to be, made of simplified model schemes representative of general classes of chemical or thermal feedback. The oregonator and Lengyel-Epstein models for the BZ and CDIMA systems have been given earlier. Pre-eminent among the more abstracted caricature models is the brusselator introduced by Prigogine and Lefever [47] which has the following form ... 

Building on similar ideas but starting from a more detailed reaction scheme, Tyson (1991) proposed a model for the mitotic oscillator based on the formation of a complex between cycUn and cdc2 kinase, followed by the activation of this complex. Essential to the oscillatory mechanism is the assumption that the active complex, i.e. MPF, promotes its own activation in a nonlinear memner. The kinetic equations, of a polynomial form, reduce under some simplifying assumptions to the equations of the two-variable Brusselator model. Inactivation of MPF is not... 

CEN EN 932-3/Al. 2003. Tests for general properties of aggregates — Part 2 Procedure and terminology for simplified petrographic description. Brussels CEN. 

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