  We consider magnetic flux moving in superconductors with periodic pinning
arrays. We show that sample heating by moving vortices produces negative
differential resistivity (NDR) of both N and S type (i.e., N- and S-shaped) in
the voltage-current characteristic (VI curve). The uniform flux flow state is
unstable in the NDR region of the VI curve. Domain structures appear during the
NDR part of the VI curve of an N type, while a filamentary instability is
observed for the NDR of an S type. The simultaneous existence of the NDR of
both types gives rise to the appearance of striking self-organized (both
stationary and non-stationary) two-dimensional dynamical structures.
