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Asymptotic properties and simulations of a stochastic logistic model under regime switching. (English) Zbl 1235.60099
Summary: Taking both white noise and colored environmental noise into account, a general stochastic logistic model under regime switching is proposed and studied. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence and global attractivity are established. The critical number between weak persistence and extinction is obtained. Moreover, some simulation figures are introduced to illustrate the main results.

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