Amplitude equations for activator-inhibitor system with superdiffusion

The generalized activator-inhibitor model with cubic nonlinearity, in which the classical Laplacian is replaced by fractional operator has been studied. The fractional operator reflects the nonlocal behavior of superdiffusion. A spatially homogeneous, time independent solution has been found and its linear stability was studied. We have also performed a weakly nonlinear analysis and obtained a system of amplitude equations that are the basis for analysing pattern formation as well as parameter regimes for which various steady-state patterns would exist.

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Math. Model. Comput. Vol. 3, No. 2, pp. 191-198 (2016)