We study the Turing bifurcation in general two-species reaction-transport systems, where particle dispersal is governed by diffusion, including cross diffusion. By performing a linear stability analysis, we find conditions for the Turing instability and compare the results with the standard Turing conditions. We apply our results to two model systems, the Lengyel-Epstein model and the Brusselator, and find strong effects of cross diffusion on the Turing bifurcation.
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Kumar et al. (2011) studied this question.
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