Noise induced patterning in reaction-diffusion systems with non-Fickian diffusion

We have studied the entropy-driven mechanism leading to stationary patterns formation in stochastic systems with local dynamics and non-Fickian diffusion. It is shown that a multiplicative noise fulfilling a fluctuation-dissipation relation is able to induce and sustain stationary structures. It was found that at small and large noise intensities the system is characterized by unstable homogeneous states. At intermediate values of the noise intensity three types of patterns are possible: nucleation, spinodal decomposition and stripes with liner defects (dislocations). Our analytical investigations are verified by computer simulations.