Dynamics and simulations of a logistic model with impulsive perturbations in a random environment

A stochastic logistic model with Markovian switching and impulsive perturbations is proposed and investigated. Firstly, we show that this model has a global and positive solution. Then we establish the sufficient conditions for extinction, non-persistence in the mean, weak persistence and stochastic permanence of the solution. The critical value between weak persistence and extinction is obtained. Afterwards we study some asymptotic properties of this model. The lower- and the upper-growth rates of the positive solution are investigated. The superior limit of the average in time of the sample path of the solution is also estimated. Finally, some simulation figures are introduced to illustrate the main results.