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Sufficient and necessary conditions of stochastic permanence and extinction for stochastic logistic populations under regime switching. (English) Zbl 1205.92058

Summary: We prove that a stochastic logistic population under regime switching controlled by a Markov chain is either stochastically permanent or extinctive, and we obtain sufficient and necessary conditions for stochastic permanence and extinction under some assumptions. In the case of stochastic permanence we estimate the limit of the average in time of the sample path of the solution by two constants related to the stationary probability distribution of the Markov chain and the parameters of the subsystems of the population model. Finally, we illustrate our conclusions through two examples.

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.)
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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