Turing Instabilities in Direction-Independent Reaction Walks

1 Turing Instabilities in Direction-Independent Reaction Walks 

Remark 10.2 These equations do not constitute a reaction-Cattaneo system because of the contribution of the intrinsic death rates f (p , Py), / = 1, 2, to the decay rate of the flows. Further, no reaction-telegraph equations can be derived for the total densities, unless the death rates /i (p , Py) are constants. 

The uniform steady state of (10.68) with boundary conditions (10.69) is given by 

This implies that the spatial modes for the densities are given by cos(kx). We write the perturbations as 

---