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On competitive Lotka-Volterra model in random environments. (English) Zbl 1182.34078

The authors study asymptotic properties of a competitive Lotka-Volterra model in random environments. A continuous-time Markov chain is used to model the random environments while the population dynamics of the different species are modelled by a regime-switching diffusion. Growth rates of the population sizes are found to be bounded above, and a partial stochastic principle of competitive exclusion is obtained.

MSC:

34F05 Ordinary differential equations and systems with randomness
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
92D25 Population dynamics (general)
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