Permanence of a stochastic delay competition model with Levy jumps

Permanence is one of the most important topics in biomathematics. The question of permanence of stochastic multi-species models is challenging because the current approaches can not be used. In this paper, an asymptotic approach is used, and sufficient criteria for permanence of a general n-species stochastic delay Lotka-Volterra competition model with Levy jumps are established. It is also shown that these criteria are sharp in some cases. The results reveal that the stochastic noises play a key role in the permanence. This approach can be also applied to investigate the permanence of other stochastic population models with/without time delay and/or Levy noises.