  We theoretically investigate the dynamical phase diagram of a one-dimensional
chain of laser-excited two-species Rydberg atoms. The existence of a variety of
unique dynamical phases in the experimentally-achievable parameter region is
predicted under the mean-field approximation, and the change of those phases
when the effect of the next-nearest neighbor interaction is included is further
discussed. In particular we find the competition of the strong Rydberg-Rydberg
interactions and the optical excitation imbalance can lead to the presence of
complex multiple chaotic phases, which are highly sensitive to the initial
Rydberg-state population and the strength of the next-nearest neighbor
interactions.
