Stability in the mean of a stochastic three species food chain model with general Le´vy jumps

A stochastic three species food chain model with general Le´vy jumps is investigated in the paper. The criterion on the global stability in the mean with probability one for each species is established. The results show that the dynamics of the model can be significantly changed by Le´vy jumps, and strongly indicate that the general jump N(dt, du) is more complicated than compensated jump N˜(dt,du).