Analysis of a stochastic delay competition system driven by Levy noise under regime switching

This paper is concerned with a stochastic delay competition system driven by Levy noise under regime switching. Both the existence and uniqueness of the global positive solution are examined. By comparison theorem, sufficient conditions for extinction and non-persistence in the mean are obtained. Some discussions are made to demonstrate that the different environment factors have significant impacts on extinction. Furthermore, we show that the global positive solution is stochastically ultimate boundedness under some conditions, and an important asymptotic property of system is given. In the end, numerical simulations are carried out to illustrate our main results.