Turing Instabilities in Direction-Dependent Reaction Walks

4 Turing Instabilities in Direction-Dependent Reaction Walks 

The kinetic terms for DDRWs, see Sect. 5.6.2, depend on the details of the underlying mechanism of the reacting system, and it is impossible to write down a general form for them. We consider here the Brusselator model. In keeping with the spirit of the model, we consider two possible direction-dependent kinetic schemes, namely an activated U2 complex or an activated UV complex, to investigate the effect of activation energy on the Turing instability [206]. 

1 Turing Instability in the Brusselator DDRW with Activated U Dimer 

If the termolecular step in the Brusselator proceeds via an activated U2 complex, we have the following kinetic scheme for the Brusselator DDRW  

Here = A, = Pj Z, and P is the steric factor and Z the collision frequency factor [350]. We consider only situations where the steric factor ensures that the kinetics are reaction-limited. We assume that the pool species A and B are in equilibrium, i.e., and 1, = p y, = jb. Then the properly 

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