A stochastic three-species food web model with Lévy jumps

For a stochastic three-species food web model with double parameters perturbation and Lévy jumps, we give the existence and uniqueness of global positive solution,which is beneficial to further study its dynamic properties. Then, by constructing Lyapunov function and applying It′s formula and Chebyshev’s inequality, it is found that the model is stochastic and ultimately bounded. Moreover, the sufficient conditions of extinction are obtained by using exponential martingale inequality and Borel-Cantelli’s lemma. Finally, some numerical simulations are introduced to illustrate the rationality of the theoretical results. The results show that the model is stochastic and ultimately bounded under the influence of Lévy noise, and large Lévy noise can lead to the extinction of populations. The algorithm has obtained good results both in theory and numerical simulations, which provides certain significance for many problems of stochastic population models.