Inhomogeneous oscillatory structures in fractional reaction–diffusion systems

We perform a study of the two component fractional reaction–diffusion system with cubic nonlinearity. The linear stage of the system stability is studied for different values of the system parameters. It is shown that for a certain value of the fractional derivatives index, a new type of instability takes place with respect to perturbations of finite wave number. As a result, inhomogeneous oscillations with this wave number become unstable and lead to nonlinear oscillations which result in spatial oscillatory structure formation.