xa + XB xa + xb none horizontal stripes vertical stripes spots

as the undetermined region in the parameter plots which we show below. The conditions for stability of these steady states are summarized in Table 5.4. By computing XA, XB and Y over a given parameter space, we can use Table 5.4 to divide this space into regions where spots, stripes, no pattern or an undetermined pattern can occur. These parameter spaces were calculated by Tyson (1996) for the system under study here and by Zhu and Murray (1995) for a simpler reaction diffusion-chemotaxis system.

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