On a stochastic logistic equation with impulsive perturbations

A stochastic logistic model with impulsive perturbations is proposed and investigated. First, we give a new definition of a solution of an impulsive stochastic differential equation (ISDE), which is more convenient for use than the existing one. Using this definition, we show that our model has a global and positive solution and obtain its explicit expression. Then we establish the sufficient conditions for extinction, non‐persistence in the mean, weak persistence, persistence in the mean and stochastic permanence of the solution. The critical value between weak persistence and extinction is obtained. In addition, the limit of the average in time of the sample path of the solution is estimated by two constants. Afterwards, the lower‐growth rate and the upper‐growth rate of the solution are estimated. Finally, sufficient conditions for global attractivity are established.