This paper reveals long time dynamics in the stochastic multimolecule
oscillatory reaction model with Poisson jumps. First, this system is
proved to have a unique global positive solution via the Lyapunov
technique. Second, the existence and uniqueness of general random
attractors for its stochastic homeomorphism flow is proved by the
comparison theorem, and meanwhile, a criterion for the existence of
singleton sets is obtained. Finally, numerical simulations are used to
illustrate the predicted random attractors.