Dynamics Analysis of a Stochastic Hybrid Logistic Model with Delay and Two-Pulse Perturbations

In this paper, we propose and discuss a stochastic logistic model with delay, Markovian switching, Levy jump, and two-pulse perturbations. First, sufficient criteria for extinction, nonpersistence in the mean, weak persistence, persistence in the mean, and stochastic permanence of the solution are gained. Then, we investigate the lower (upper) growth rate of the solutions. At last, we make use of Matlab to illustrate the main results and give an explanation of biological implications: the large stochastic disturbances are disadvantageous for the persistence of the population; excessive impulsive harvesting or toxin input can lead to extinction of the population.