New type of instability in fractional reaction-diffusion systems

V. V. Gafiychuk, B. Y. Datsko


The linear stage of the two-component fractional reaction-diffusion system stability is studied. It is shown that for certain value of fractional derivative index a new type of instability takes place and the system becomes unstable towards perturbations of finite wave number become unstable and lead to non-linear oscillations which result in spatial oscillatory structure formation. Computer simulation of the system for cubic non-linearity is performed.

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