Turing Instability in the Standard Brusselator Reaction-Diffusion System

3 Turing Instability in the Standard Brusselator Reaction-Diffusion System 

We use the Brusselator, see Sect. 1.4.4, to illustrate these results. The steady state of the well-mixed system is stable ifb = 1 + see (1.83). Condition (10.35) implies that 

The second inequality is satisfied if the uniform steady state (PuU)- P (x)) = (a, h/a) is stable against uniform perturbation, that isb b. The Turing condition (10.40) reads 

If we consider b to be the control parameter, then the threshold for the Turing instability is given by 

In order for the Turing bifureation to occur first, the Turing threshold must lie below the Hopf threshold of the well-mixed system, b - bn- 

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