Asymptotic behavior of a delayed stochastic logistic model with impulsive perturbations

In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results.