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Stochastic population dynamics under regime switching. (English) Zbl 1113.92052
Summary: We develop a new stochastic population model under regime switching. Our model takes both white and color environmental noises into account. We show that the white noise suppresses explosions in population dynamics. Moreover, from the point of population dynamics, our new model has more desired properties than some existing stochastic population models. In particular, we show that our model is stochastically ultimately bounded.

MSC:
92D25Population dynamics (general)
60H30Applications of stochastic analysis
60J20Applications of Markov chains and discrete-time Markov processes on general state spaces
60H10Stochastic ordinary differential equations