On a nonautonomous competitive system subject to stochastic and impulsive perturbations

•A nonautonomous impulsive stochastic competitive system is considered.•Sufficient conditions for stochastic permanence and extinction are established.•The influences of stochastic and impulsive perturbations are shown.

This paper presents a nonautonomous impulsive stochastic differential model of competition between species which contains the classic two-species competitive Lotka-Volterra model as a special case. With the theory of impulsive stochastic differential equations, a good understanding of stochastic permanence and extinction of system is obtained. Two specific numerical examples are presented to support the analytical results. Conclusions are also given.