Long-time dynamics of a stochastic multimolecule oscillatory reaction model with Poisson jumps

Abstract

<abstract><p>This paper reveals dynamical behaviors 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.</p></abstract>