  This paper develops stability and stabilization results for systems of fully
coupled jump diffusions. Such systems frequently arise in numerous applications
where each subsystem (component) is operated under the influence of other
subsystems (components). This paper derives sufficient conditions under which
the underlying coupled jump diffusion is stable. The results are then applied
to investigate the stability of linearizable jump diffusions, fast-slow coupled
jump diffusions. Moreover, weak stabilization of interacting systems and
consensus of leader-following systems are examined.
