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Logistic models with regime switching: permanence and ergodicity. (English) Zbl 1357.92064

Summary: Focusing on stochastic dynamics involving continuous states as well as discrete events, this paper investigates stochastic logistic model with regime switching and obtains sufficient conditions for stochastic permanence, which are much weaker than the existing results in the literature. Furthermore, under the conditions of stochastic permanence, the existence and uniqueness of stationary distribution is proved. An interesting fact is: The regime switching can suppress the non-permanence. A couple of examples and numerical simulations are given to illustrate our results.

MSC:

92D25 Population dynamics (general)
60J20 Applications of Markov chains and discrete-time Markov processes on general state spaces (social mobility, learning theory, industrial processes, etc.)
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