The paper is devoted to variational analysis of set-valued mappings acting from quasimetric spaces into topological spaces with variable ordering structures. Besides the mathematical novelty, our motivation comes from applications to adaptive dynamical models of behavioral sciences. We develop a unified dynamical approach to variational principles in such settings based on the new minimal point theorem for product sets with general ordering. This approach allows us, in particular, to establish enhanced versions of the Ekeland variational principle for set-valued mappings ordered by variable preference.