Asymptotic properties and simulations of a stochastic logistic model under regime switching II

This is a continuation of our paper [M. Liu, K. Wang, Asymptotic properties and simulations of a stochastic logistic model under regime switching, Math. Comput. Modelling 54 (2011) 2139–2154]. First, we establish the sufficient conditions for stochastic permanence which are much weaker than those in our previous paper. Then we study some new asymptotic properties of this model. The lower-growth rate and the upper-growth rate 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. Some recent investigations are improved and generalized.