Survival analysis of stochastic three-species food chain model with white noise and general Lévy jumps

The survival of a stochastic three species food chain model with white noise and general Lévy jumps was analyzed, which includes existence and uniqueness of global positive solution as well as permanence in the mean of the highest species.Situations where some species are extinct while others are persistent in the mean were also clarified.The results show that Lévy jumps can obviously change the survival of population, which can make the persistent population become extinct, or vice versa.