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Asymptotic properties and simulations of a stochastic logistic model under regime switching II. (English) Zbl 1255.60129
Summary: This is a continuation of our paper [Math. Comput. Modelling 54, No. 9–10, 2139–2154 (2011; Zbl 1235.60099)]. 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.

60J28 Applications of continuous-time Markov processes on discrete state spaces
34D05 Asymptotic properties of solutions to ordinary differential equations
92D40 Ecology
34F05 Ordinary differential equations and systems with randomness
Full Text: DOI
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