  We study the dynamics of a class-B semiconductor microring laser coupled to a
neutral microring resonator for common fabrication parameters. For zero
detuning between the resonators, we identify five dynamical regions controlled
by the normalized pump rate of the laser and coupling strength between the
resonators. These regions show stable lasing with phase locking for either
sufficiently small or large coupling strength parameter values. Multistability
and chaos arise in between these stable regions where at least one fixed point
is attractive. The transition from stable to unstable lasing regions in the
parameter space phase diagram is a crossover.
