Localization of eigenvectors in random graphs

We consider spatial organization of point defects in the generalized model of defects formation in elastic medium by taking into account defects production by irradiation influence and stochastic contribution for defects dynamics satisfying the fluctuation dissipation relation. We have found that depending on initial conditions and control parameters reduced to defects generation rate caused by irradiation, temperature and the stochastic source intensity different stationary structures of defects can be organized during the system evolution. Studying phase transitions between phases characterized by low- and high defect densities in stochastic system we have shown that such phenomena are described by mechanisms inherent in entropy-driven phase transitions. Stationary patterns are studied by amplitude analysis of unstable slow modes.