The Brusselator system and oscillations

Example 13.3 The Brusselator system and oscillations One theoretical model displaying order in time is the Brusselator scheme, which was introduced in Section 12.7.1. In the limit of irreversible reactions the Brusselator scheme is 

When the concentrations of A and B are controlled, the kinetic equations for intermediate components X and Y are 

These equations have the following stationary(s) solutions 

Equation (12.93) shows that Det 0 as long as B k4/k2 + (k3/k2)X2 and the system remains stable, otherwise instability arises, and the system undergoes a Hopf bifurcation at 

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