Analysis of impulsive stochastic delay budworm population model with Le´vy jumps

In this paper, two types impulsive delay stochastic budworm population models are proposed and investigated. Based on some standard assumptions, a series sufficient criteria about long time behavior of the solutions are given. For the unbounded positive impulse, we obtain a sufficient criteria that makes the solution weakly permanent, which is close to the necessary criterion. Then, we demonstrate the conditions that produce the solutions are stochastically permanent when positive impulse is bounded. Finally, numerical simulations of the model confirms our theoretical results. Our rsults improve and extend some previous results.