Abstract
In this paper possible scenarios of pattern formation in nonlinear media with diffusion and differential operators of a noninteger order are studied for the abstract Brusselator model. Through the standard linear analysis exact critical values for different types of instabilities are derived. It is shown that the stability criteria significantly depend on the order of the fractional derivative in the case of the Hopf and C2TH bifurcations. Predictions of the linear theory are confirmed by the numerical simulation.
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