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

Abstract

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.

Keywords

• multimolecule oscillatory reaction model
• random attractors
• uniqueness
• singleton sets